-
question_answer1)
If the latus rectum of an ellipse be equal to half of its minor axis, then its eccentricity is [MP PET 1991, 97; Karnataka CET 2000]
A)
3/2 done
clear
B)
\[\sqrt{3}/2\] done
clear
C)
2/3 done
clear
D)
\[\sqrt{2}/3\] done
clear
View Solution play_arrow
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question_answer2)
If distance between the directrices be thrice the distance between the foci, then eccentricity of ellipse is
A)
1/2 done
clear
B)
2/3 done
clear
C)
\[1/\sqrt{3}\] done
clear
D)
4/5 done
clear
View Solution play_arrow
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question_answer3)
The equation of the ellipse whose centre is at origin and which passes through the points (?3, 1) and (2, ?2) is
A)
\[5{{x}^{2}}+3{{y}^{2}}=32\] done
clear
B)
\[3{{x}^{2}}+5{{y}^{2}}=32\] done
clear
C)
\[5{{x}^{2}}-3{{y}^{2}}=32\] done
clear
D)
\[3{{x}^{2}}+5{{y}^{2}}+32=0\] done
clear
View Solution play_arrow
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question_answer4)
If the eccentricity of an ellipse be 5/8 and the distance between its foci be 10, then its latus rectum is
A)
39/4 done
clear
B)
12 done
clear
C)
15 done
clear
D)
37/2 done
clear
View Solution play_arrow
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question_answer5)
If the foci and vertices of an ellipse be \[(\pm 1,\ 0)\] and \[(\pm 2,\ 0)\], then the minor axis of the ellipse is
A)
\[2\sqrt{5}\] done
clear
B)
2 done
clear
C)
4 done
clear
D)
\[2\sqrt{3}\] done
clear
View Solution play_arrow
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question_answer6)
The equations of the directrices of the ellipse \[16{{x}^{2}}+25{{y}^{2}}=400\] are
A)
\[2x=\pm 25\] done
clear
B)
\[5x=\pm 9\] done
clear
C)
\[3x=\pm 10\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer7)
The eccentricity of an ellipse is 2/3, latus rectum is 5 and centre is (0, 0). The equation of the ellipse is
A)
\[\frac{{{x}^{2}}}{81}+\frac{{{y}^{2}}}{45}=1\] done
clear
B)
\[\frac{4{{x}^{2}}}{81}+\frac{4{{y}^{2}}}{45}=1\] done
clear
C)
\[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{5}=1\] done
clear
D)
\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] done
clear
View Solution play_arrow
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question_answer8)
The latus rectum of an ellipse is 10 and the minor axis is equal to the distance between the foci. The equation of the ellipse is
A)
\[{{x}^{2}}+2{{y}^{2}}=100\] done
clear
B)
\[{{x}^{2}}+\sqrt{2}{{y}^{2}}=10\] done
clear
C)
\[{{x}^{2}}-2{{y}^{2}}=100\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer9)
The distance between the directrices of the ellipse \[\frac{{{x}^{2}}}{36}+\frac{{{y}^{2}}}{20}=1\] is
A)
8 done
clear
B)
12 done
clear
C)
18 done
clear
D)
24 done
clear
View Solution play_arrow
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question_answer10)
The distance between the foci of the ellipse \[3{{x}^{2}}+4{{y}^{2}}=48\] is
A)
2 done
clear
B)
4 done
clear
C)
6 done
clear
D)
8 done
clear
View Solution play_arrow
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question_answer11)
The equation of the ellipse whose vertices are \[(\pm 5,\ 0)\] and foci are \[(\pm 4,\ 0)\] is
A)
\[9{{x}^{2}}+25{{y}^{2}}=225\] done
clear
B)
\[25{{x}^{2}}+9{{y}^{2}}=225\] done
clear
C)
\[3{{x}^{2}}+4{{y}^{2}}=192\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer12)
The equation of the ellipse whose foci are \[(\pm 5,\ 0)\] and one of its directrix is \[5x=36\], is
A)
\[\frac{{{x}^{2}}}{36}+\frac{{{y}^{2}}}{11}=1\] done
clear
B)
\[\frac{{{x}^{2}}}{6}+\frac{{{y}^{2}}}{\sqrt{11}}=1\] done
clear
C)
\[\frac{{{x}^{2}}}{6}+\frac{{{y}^{2}}}{11}=1\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer13)
If the eccentricity of an ellipse be \[1/\sqrt{2}\], then its latus rectum is equal to its
A)
Minor axis done
clear
B)
Semi-minor axis done
clear
C)
Major axis done
clear
D)
Semi-major axis done
clear
View Solution play_arrow
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question_answer14)
The length of the latus rectum of the ellipse \[5{{x}^{2}}+9{{y}^{2}}=45\] is [MNR 1978, 80, 81]
A)
\[\sqrt{5}/4\] done
clear
B)
\[\sqrt{5}/2\] done
clear
C)
5/3 done
clear
D)
10/3 done
clear
View Solution play_arrow
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question_answer15)
If the distance between a focus and corresponding directrix of an ellipse be 8 and the eccentricity be 1/2, then length of the minor axis is
A)
3 done
clear
B)
\[4\sqrt{2}\] done
clear
C)
6 done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer16)
Eccentricity of the conic \[16{{x}^{2}}+7{{y}^{2}}=112\]is [MNR 1981]
A)
\[3/\sqrt{7}\] done
clear
B)
7/16 done
clear
C)
3/4 done
clear
D)
4/3 done
clear
View Solution play_arrow
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question_answer17)
If the distance between the foci of an ellipse be equal to its minor axis, then its eccentricity is
A)
1/2 done
clear
B)
\[1/\sqrt{2}\] done
clear
C)
1/3 done
clear
D)
\[1/\sqrt{3}\] done
clear
View Solution play_arrow
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question_answer18)
An ellipse passes through the point (?3, 1) and its eccentricity is \[\sqrt{\frac{2}{5}}\]. The equation of the ellipse is
A)
\[3{{x}^{2}}+5{{y}^{2}}=32\] done
clear
B)
\[3{{x}^{2}}+5{{y}^{2}}=25\] done
clear
C)
\[3{{x}^{2}}+{{y}^{2}}=4\] done
clear
D)
\[3{{x}^{2}}+{{y}^{2}}=9\] done
clear
View Solution play_arrow
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question_answer19)
The lengths of major and minor axis of an ellipse are 10 and 8 respectively and its major axis along the y-axis. The equation of the ellipse referred to its centre as origin is [Pb. CET 2003]
A)
\[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\] done
clear
B)
\[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{25}=1\] done
clear
C)
\[\frac{{{x}^{2}}}{100}+\frac{{{y}^{2}}}{64}=1\] done
clear
D)
\[\frac{{{x}^{2}}}{64}+\frac{{{y}^{2}}}{100}=1\] done
clear
View Solution play_arrow
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question_answer20)
If the centre, one of the foci and semi-major axis of an ellipse be (0, 0), (0, 3) and 5 then its equation is [AMU 1981]
A)
\[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{25}=1\] done
clear
B)
\[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\] done
clear
C)
\[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{25}=1\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer21)
The equation of the ellipse whose one of the vertices is (0,7) and the corresponding directrix is \[y=12\], is
A)
\[95{{x}^{2}}+144{{y}^{2}}=4655\] done
clear
B)
\[144{{x}^{2}}+95{{y}^{2}}=4655\] done
clear
C)
\[95{{x}^{2}}+144{{y}^{2}}=13680\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer22)
The equation \[2{{x}^{2}}+3{{y}^{2}}=30\] represents [MP PET 1988]
A)
A circle done
clear
B)
An ellipse done
clear
C)
A hyperbola done
clear
D)
A parabola done
clear
View Solution play_arrow
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question_answer23)
hThe equation of the ellipse whose latus rectum is 8 and whose eccentricity is \[\frac{1}{\sqrt{2}}\], referred to the principal axes of coordinates, is [MP PET 1993]
A)
\[\frac{{{x}^{2}}}{18}+\frac{{{y}^{2}}}{32}=1\] done
clear
B)
\[\frac{{{x}^{2}}}{8}+\frac{{{y}^{2}}}{9}=1\] done
clear
C)
\[\frac{{{x}^{2}}}{64}+\frac{{{y}^{2}}}{32}=1\] done
clear
D)
\[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{24}=1\] done
clear
View Solution play_arrow
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question_answer24)
Eccentricity of the ellipse whose latus rectum is equal to the distance between two focus points, is
A)
\[\frac{\sqrt{5}+1}{2}\] done
clear
B)
\[9{{x}^{2}}+5{{y}^{2}}-30y=0\] done
clear
C)
\[\frac{\sqrt{5}}{2}\] done
clear
D)
\[\frac{\sqrt{3}}{2}\] done
clear
View Solution play_arrow
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question_answer25)
For the ellipse \[3{{x}^{2}}+4{{y}^{2}}=12\], the length of latus rectum is [MNR 1973]
A)
\[\frac{3}{2}\] done
clear
B)
3 done
clear
C)
\[\frac{8}{3}\] done
clear
D)
\[\sqrt{\frac{3}{2}}\] done
clear
View Solution play_arrow
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question_answer26)
For the ellipse \[\frac{{{x}^{2}}}{64}+\frac{{{y}^{2}}}{28}=1\], the eccentricity is [MNR 1974]
A)
\[\frac{3}{4}\] done
clear
B)
\[\frac{4}{3}\] done
clear
C)
\[\frac{1}{\sqrt{7}}\] done
clear
D)
\[\frac{{{x}^{2}}}{4}+{{y}^{2}}=1\] done
clear
View Solution play_arrow
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question_answer27)
If the length of the major axis of an ellipse is three times the length of its minor axis, then its eccentricity is [EAMCET 1990]
A)
\[\frac{1}{3}\] done
clear
B)
\[\frac{1}{\sqrt{3}}\] done
clear
C)
\[\frac{1}{\sqrt{2}}\] done
clear
D)
\[\frac{2\sqrt{2}}{3}\] done
clear
View Solution play_arrow
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question_answer28)
The length of the latus rectum of an ellipse is \[\frac{1}{3}\] of the major axis. Its eccentricity is [EAMCET 1991]
A)
\[\frac{2}{3}\] done
clear
B)
\[\sqrt{\frac{2}{3}}\] done
clear
C)
\[\frac{5\times 4\times 3}{{{7}^{3}}}\] done
clear
D)
\[{{\left( \frac{3}{4} \right)}^{4}}\] done
clear
View Solution play_arrow
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question_answer29)
An ellipse is described by using an endless string which is passed over two pins. If the axes are 6 cm and 4 cm, the necessary length of the string and the distance between the pins respectively in cm, are [MNR 1989]
A)
\[6,\ 2\sqrt{5}\] done
clear
B)
\[6,\ \sqrt{5}\] done
clear
C)
\[4,\ 2\sqrt{5}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer30)
The equation \[\frac{{{x}^{2}}}{2-r}+\frac{{{y}^{2}}}{r-5}+1=0\] represents an ellipse, if [MP PET 1995]
A)
\[r>2\] done
clear
B)
\[2<r<5\] done
clear
C)
\[r>5\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer31)
The locus of the point of intersection of perpendicular tangents to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\], is [MP PET 1995]
A)
\[{{x}^{2}}+{{y}^{2}}={{a}^{2}}-{{b}^{2}}\] done
clear
B)
\[{{x}^{2}}-{{y}^{2}}={{a}^{2}}-{{b}^{2}}\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}={{a}^{2}}+{{b}^{2}}\] done
clear
D)
\[{{x}^{2}}-{{y}^{2}}={{a}^{2}}+{{b}^{2}}\] done
clear
View Solution play_arrow
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question_answer32)
The length of the latus rectum of the ellipse \[\frac{{{x}^{2}}}{36}+\frac{{{y}^{2}}}{49}=1\] [Karnataka CET 1993]
A)
98/6 done
clear
B)
72/7 done
clear
C)
72/14 done
clear
D)
98/12 done
clear
View Solution play_arrow
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question_answer33)
The distance of the point \['\theta '\]on the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] from a focus is
A)
\[a(e+\cos \theta )\] done
clear
B)
\[a(e-\cos \theta )\] done
clear
C)
\[a(1+e\cos \theta )\] done
clear
D)
\[a(1+2e\cos \theta )\] done
clear
View Solution play_arrow
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question_answer34)
The equation of the ellipse whose one focus is at (4, 0) and whose eccentricity is 4/5, is [Karnataka CET 1993]
A)
\[\frac{{{x}^{2}}}{{{3}^{2}}}+\frac{{{y}^{2}}}{{{5}^{2}}}=1\] done
clear
B)
\[\frac{{{x}^{2}}}{{{5}^{2}}}+\frac{{{y}^{2}}}{{{3}^{2}}}=1\] done
clear
C)
\[\frac{{{x}^{2}}}{{{5}^{2}}}+\frac{{{y}^{2}}}{{{4}^{2}}}=1\] done
clear
D)
\[\frac{{{x}^{2}}}{{{4}^{2}}}+\frac{{{y}^{2}}}{{{5}^{2}}}=1\] done
clear
View Solution play_arrow
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question_answer35)
The foci of \[16{{x}^{2}}+25{{y}^{2}}=400\] are [BIT Ranchi 1996]
A)
\[(\pm 3,\ 0)\] done
clear
B)
\[(0,\ \pm 3)\] done
clear
C)
\[(3,\ -3)\] done
clear
D)
\[(-3,\ 3)\] done
clear
View Solution play_arrow
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question_answer36)
Eccentricity of the ellipse \[9{{x}^{2}}+25{{y}^{2}}=225\] is [Kerala (Engg.) 2002]
A)
\[\frac{3}{5}\] done
clear
B)
\[\frac{4}{5}\] done
clear
C)
\[\frac{9}{25}\] done
clear
D)
\[\frac{\sqrt{34}}{5}\] done
clear
View Solution play_arrow
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question_answer37)
The eccentricity of the ellipse \[25{{x}^{2}}+16{{y}^{2}}=100\], is
A)
\[\frac{5}{14}\] done
clear
B)
\[\frac{4}{5}\] done
clear
C)
\[\frac{3}{5}\] done
clear
D)
\[\frac{2}{5}\] done
clear
View Solution play_arrow
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question_answer38)
The length of the latus rectum of the ellipse \[9{{x}^{2}}+4{{y}^{2}}=1\], is [MP PET 1999]
A)
\[\frac{3}{2}\] done
clear
B)
\[\frac{8}{3}\] done
clear
C)
\[\frac{4}{9}\] done
clear
D)
\[\frac{8}{9}\] done
clear
View Solution play_arrow
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question_answer39)
The locus of a variable point whose distance from (?2, 0) is \[\frac{2}{3}\] times its distance from the line \[x=-\frac{9}{2}\], is [IIT 1994]
A)
Ellipse done
clear
B)
Parabola done
clear
C)
Hyperbola done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer40)
If \[P\equiv (x,\ y)\], \[{{F}_{1}}\equiv (3,\ 0)\], \[{{F}_{2}}\equiv (-3,\ 0)\] and \[16{{x}^{2}}+25{{y}^{2}}=400\], then \[P{{F}_{1}}+P{{F}_{2}}\] equals [IIT 1998]
A)
8 done
clear
B)
6 done
clear
C)
10 done
clear
D)
12 done
clear
View Solution play_arrow
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question_answer41)
P is any point on the ellipse\[9{{x}^{2}}+36{{y}^{2}}=324\]., whose foci are S and S?. Then \[SP+S'P\] equals [DCE 1999]
A)
3 done
clear
B)
12 done
clear
C)
36 done
clear
D)
324 done
clear
View Solution play_arrow
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question_answer42)
What is the equation of the ellipse with foci \[(\pm 2,\ 0)\] and eccentricity \[=\frac{1}{2}\] [DCE 1999]
A)
\[3{{x}^{2}}+4{{y}^{2}}=48\] done
clear
B)
\[4{{x}^{2}}+3{{y}^{2}}=48\] done
clear
C)
\[3{{x}^{2}}+4{{y}^{2}}=0\] done
clear
D)
\[4{{x}^{2}}+3{{y}^{2}}=0\] done
clear
View Solution play_arrow
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question_answer43)
The eccentricity of the ellipse \[4{{x}^{2}}+9{{y}^{2}}=36\], is [MP PET 2000]
A)
\[\frac{1}{2\sqrt{3}}\] done
clear
B)
\[\frac{1}{\sqrt{3}}\] done
clear
C)
\[\frac{\sqrt{5}}{3}\] done
clear
D)
\[\frac{\sqrt{5}}{6}\] done
clear
View Solution play_arrow
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question_answer44)
The eccentricity of the ellipse \[25{{x}^{2}}+16{{y}^{2}}=400\] is [MP PET 2001]
A)
3/5 done
clear
B)
1/3 done
clear
C)
2/5 done
clear
D)
1/5 done
clear
View Solution play_arrow
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question_answer45)
The distance between the foci of an ellipse is 16 and eccentricity is \[\frac{1}{2}\]. Length of the major axis of the ellipse is [Karnataka CET 2001]
A)
8 done
clear
B)
64 done
clear
C)
16 done
clear
D)
32 done
clear
View Solution play_arrow
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question_answer46)
If the eccentricity of the two ellipse \[\frac{{{x}^{2}}}{169}+\frac{{{y}^{2}}}{25}=1\]and \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] are equal, then the value of \[a/b\] is [UPSEAT 2001]
A)
5/13 done
clear
B)
6/13 done
clear
C)
13/5 done
clear
D)
13/6 done
clear
View Solution play_arrow
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question_answer47)
In the ellipse, minor axis is 8 and eccentricity is \[\frac{\sqrt{5}}{3}\]. Then major axis is [Karnataka CET 2002]
A)
6 done
clear
B)
12 done
clear
C)
10 done
clear
D)
16 done
clear
View Solution play_arrow
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question_answer48)
In an ellipse \[9{{x}^{2}}+5{{y}^{2}}=45\], the distance between the foci is [Karnataka CET 2002]
A)
\[4\sqrt{5}\] done
clear
B)
\[\frac{49}{4}{{x}^{2}}-\frac{51}{196}{{y}^{2}}=1\] done
clear
C)
3 done
clear
D)
4 done
clear
View Solution play_arrow
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question_answer49)
Equation of the ellipse with eccentricity \[\frac{1}{2}\] and foci at \[(\pm 1,\ 0)\] is [MP PET 2002]
A)
\[\frac{{{x}^{2}}}{3}+\frac{{{y}^{2}}}{4}=1\] done
clear
B)
\[\frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{3}=1\] done
clear
C)
\[\frac{{{x}^{2}}}{3}+\frac{{{y}^{2}}}{4}=\frac{4}{3}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer50)
The sum of focal distances of any point on the ellipse with major and minor axes as 2a and 2b respectively, is equal to [MP PET 2003]
A)
2a done
clear
B)
\[\frac{2a}{b}\] done
clear
C)
\[\frac{2b}{a}\] done
clear
D)
\[\frac{{{b}^{2}}}{a}\] done
clear
View Solution play_arrow
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question_answer51)
The equation of ellipse whose distance between the foci is equal to 8 and distance between the directrix is 18, is
A)
\[5{{x}^{2}}-9{{y}^{2}}=180\] done
clear
B)
\[9{{x}^{2}}+5{{y}^{2}}=180\] done
clear
C)
\[{{x}^{2}}+9{{y}^{2}}=180\] done
clear
D)
\[5{{x}^{2}}+9{{y}^{2}}=180\] done
clear
View Solution play_arrow
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question_answer52)
In an ellipse the distance between its foci is 6 and its minor axis is 8. Then its eccentricity is [EAMCET 1994]
A)
\[\frac{4}{5}\] done
clear
B)
\[\frac{1}{\sqrt{52}}\] done
clear
C)
\[\frac{3}{5}\] done
clear
D)
\[25{{x}^{2}}+144{{y}^{2}}=900\] done
clear
View Solution play_arrow
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question_answer53)
If a bar of given length moves with its extremities on two fixed straight lines at right angles, then the locus of any point on bar marked on the bar describes a/an [Orissa JEE 2003]
A)
Circle done
clear
B)
Parabola done
clear
C)
Ellipse done
clear
D)
Hyperbola done
clear
View Solution play_arrow
-
question_answer54)
The centre of the ellipse \[4{{x}^{2}}+9{{y}^{2}}-16x-54y+61=0\] is [MP PET 1992]
A)
(1, 3) done
clear
B)
(2, 3) done
clear
C)
(3, 2) done
clear
D)
(3, 1) done
clear
View Solution play_arrow
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question_answer55)
Latus rectum of ellipse \[4{{x}^{2}}+9{{y}^{2}}-8x-36y+4=0\] is [MP PET 1989]
A)
8/3 done
clear
B)
4/3 done
clear
C)
\[\frac{\sqrt{5}}{3}\] done
clear
D)
16/3 done
clear
View Solution play_arrow
-
question_answer56)
Eccentricity of the ellipse \[4{{x}^{2}}+{{y}^{2}}-8x+2y+1=0\] is
A)
\[1/\sqrt{3}\] done
clear
B)
\[\sqrt{3}/2\] done
clear
C)
\[1/2\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer57)
The equation of an ellipse whose eccentricity is 1/2 and the vertices are (4, 0) and (10, 0) is
A)
\[3{{x}^{2}}+4{{y}^{2}}-42x+120=0\] done
clear
B)
\[3{{x}^{2}}+4{{y}^{2}}+42x+120=0\] done
clear
C)
\[3{{x}^{2}}+4{{y}^{2}}+42x-120=0\] done
clear
D)
\[3{{x}^{2}}+4{{y}^{2}}-42x-120=0\] done
clear
View Solution play_arrow
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question_answer58)
The equation of the ellipse whose centre is (2, ?3), one of the foci is (3, ?3) and the corresponding vertex is (4, ?3) is
A)
\[\frac{{{(x-2)}^{2}}}{3}+\frac{{{(y+3)}^{2}}}{4}=1\] done
clear
B)
\[\frac{{{(x-2)}^{2}}}{4}+\frac{{{(y+3)}^{2}}}{3}=1\] done
clear
C)
\[\frac{{{x}^{2}}}{3}+\frac{{{y}^{2}}}{4}=1\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer59)
The equation \[14{{x}^{2}}-4xy+11{{y}^{2}}-44x-58y+71=0\] represents [BIT Ranchi 1986]
A)
A circle done
clear
B)
An ellipse done
clear
C)
A hyperbola done
clear
D)
A rectangular hyperbola done
clear
View Solution play_arrow
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question_answer60)
The centre of the ellipse\[\frac{{{(x+y-2)}^{2}}}{9}+\frac{{{(x-y)}^{2}}}{16}=1\] is [EAMCET 1994]
A)
(0, 0) done
clear
B)
(1, 1) done
clear
C)
(1, 0) done
clear
D)
(0, 1) done
clear
View Solution play_arrow
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question_answer61)
The equation of an ellipse whose focus (?1, 1), whose directrix is \[x-y+3=0\] and whose eccentricity is \[\frac{1}{2}\], is given by [MP PET 1993]
A)
\[7{{x}^{2}}+2xy+7{{y}^{2}}+10x-10y+7=0\] done
clear
B)
\[7{{x}^{2}}-2xy+7{{y}^{2}}-10x+10y+7=0\] done
clear
C)
\[7{{x}^{2}}-2xy+7{{y}^{2}}-10x-10y-7=0\] done
clear
D)
\[7{{x}^{2}}-2xy+7{{y}^{2}}+10x+10y-7=0\] done
clear
View Solution play_arrow
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question_answer62)
The foci of the ellipse \[25{{(x+1)}^{2}}+9{{(y+2)}^{2}}=225\] are at [MNR 1991; MP PET 1998; UPSEAT 2000]
A)
(?1, 2) and (?1, ?6) done
clear
B)
(?1, 2) and (6, 1) done
clear
C)
(1, ?2) and (1, ?6) done
clear
D)
(?1, ?2) and (1, 6) done
clear
View Solution play_arrow
-
question_answer63)
The eccentricity of the ellipse \[9{{x}^{2}}+5{{y}^{2}}-30y=0\], is [MNR 1993; Pb. CET 2004]
A)
1/3 done
clear
B)
2/3 done
clear
C)
3/4 done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer64)
The curve represented by \[x=3(\cos t+\sin t)\], \[y=4(\cos t-\sin t)\] is [EAMCET 1988; DCE 2000]
A)
Ellipse done
clear
B)
Parabola done
clear
C)
Hyperbola done
clear
D)
Circle done
clear
View Solution play_arrow
-
question_answer65)
Equation \[x=a\cos \theta ,\ y=b\sin \theta (a>b)\] represent a conic section whose eccentricity e is given by
A)
\[{{e}^{2}}=\frac{{{a}^{2}}+{{b}^{2}}}{{{a}^{2}}}\] done
clear
B)
\[{{e}^{2}}=\frac{{{a}^{2}}+{{b}^{2}}}{{{b}^{2}}}\] done
clear
C)
\[{{e}^{2}}=\frac{{{a}^{2}}-{{b}^{2}}}{{{a}^{2}}}\] done
clear
D)
\[{{e}^{2}}=\frac{{{a}^{2}}-{{b}^{2}}}{{{b}^{2}}}\] done
clear
View Solution play_arrow
-
question_answer66)
The eccentricity of the ellipse \[4{{x}^{2}}+9{{y}^{2}}+8x+36y+4=0\] is [MP PET 1996]
A)
\[\frac{5}{6}\] done
clear
B)
\[\frac{3}{5}\] done
clear
C)
\[\frac{\sqrt{2}}{3}\] done
clear
D)
\[\frac{\sqrt{5}}{3}\] done
clear
View Solution play_arrow
-
question_answer67)
The co-ordinates of the foci of the ellipse \[3{{x}^{2}}+4{{y}^{2}}-12x-8y+4=0\] are
A)
(1, 2), (3, 4) done
clear
B)
(1, 4), (3, 1) done
clear
C)
(1, 1), (3, 1) done
clear
D)
(2, 3), (5, 4) done
clear
View Solution play_arrow
-
question_answer68)
The eccentricity of the curve represented by the equation \[{{x}^{2}}+2{{y}^{2}}-2x+3y+2=0\] is [Roorkee 1998]
A)
0 done
clear
B)
1/2 done
clear
C)
\[1/\sqrt{2}\] done
clear
D)
\[\sqrt{2}\] done
clear
View Solution play_arrow
-
question_answer69)
For the ellipse \[25{{x}^{2}}+9{{y}^{2}}-150x-90y+225=0\]the eccentricity \[e=\] [Karnataka CET 2004]
A)
2/5 done
clear
B)
3/5 done
clear
C)
4/5 done
clear
D)
1/5 done
clear
View Solution play_arrow
-
question_answer70)
The eccentricity of the ellipse \[\frac{{{(x-1)}^{2}}}{9}+\frac{{{(y+1)}^{2}}}{25}=1\] is [AMU 1999]
A)
4/5 done
clear
B)
3/5 done
clear
C)
5/4 done
clear
D)
Imaginary done
clear
View Solution play_arrow
-
question_answer71)
The length of the axes of the conic \[9{{x}^{2}}+4{{y}^{2}}-6x+4y+1=0\], are [Orissa JEE 2002]
A)
\[\frac{1}{2},\ 9\] done
clear
B)
\[3,\ \frac{2}{5}\] done
clear
C)
\[1,\ \frac{2}{3}\] done
clear
D)
3, 2 done
clear
View Solution play_arrow
-
question_answer72)
The eccentricity of the ellipse \[9{{x}^{2}}+5{{y}^{2}}-18x-2y-16=0\] is [EAMCET 2003]
A)
1/2 done
clear
B)
2/3 done
clear
C)
1/3 done
clear
D)
3/4 done
clear
View Solution play_arrow
-
question_answer73)
The eccentricity of the conic \[4{{x}^{2}}+16{{y}^{2}}-24x-3y=1\] is [MP PET 2004]
A)
\[\frac{\sqrt{3}}{2}\] done
clear
B)
\[\frac{1}{2}\] done
clear
C)
\[\frac{\sqrt{3}}{4}\] done
clear
D)
\[\sqrt{3}\] done
clear
View Solution play_arrow
-
question_answer74)
If the line \[y=2x+c\] be a tangent to the ellipse \[\frac{{{x}^{2}}}{8}+\frac{{{y}^{2}}}{4}=1\], then \[c=\] [MNR 1979; DCE 2000]
A)
\[\pm 4\] done
clear
B)
\[\pm 6\] done
clear
C)
\[\pm 1\] done
clear
D)
\[\pm 8\] done
clear
View Solution play_arrow
-
question_answer75)
The position of the point (4, ?3) with respect to the ellipse \[2{{x}^{2}}+5{{y}^{2}}=20\] is
A)
Outside the ellipse done
clear
B)
On the ellipse done
clear
C)
On the major axis done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer76)
The equation of the tangent to the ellipse \[{{x}^{2}}+16{{y}^{2}}=16\] making an angle of \[{{60}^{o}}\]with x-axis is
A)
\[\sqrt{3}x-y+7=0\] done
clear
B)
\[\sqrt{3}x-y-7=0\] done
clear
C)
\[\sqrt{3}x-y\pm 7=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer77)
The position of the point (1, 3) with respect to the ellipse \[4{{x}^{2}}+9{{y}^{2}}-16x-54y+61=0\] [MP PET 1991]
A)
Outside the ellipse done
clear
B)
On the ellipse done
clear
C)
On the major axis done
clear
D)
On the minor axis done
clear
View Solution play_arrow
-
question_answer78)
The line \[lx+my-n=0\] will be tangent to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\], if
A)
\[{{a}^{2}}{{l}^{2}}+{{b}^{2}}{{m}^{2}}={{n}^{2}}\] done
clear
B)
\[a{{l}^{2}}+b{{m}^{2}}={{n}^{2}}\] done
clear
C)
\[{{a}^{2}}l+{{b}^{2}}m=n\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer79)
The locus of the point of intersection of mutually perpendicular tangent to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\], is
A)
A straight line done
clear
B)
A parabola done
clear
C)
A circle done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer80)
The equation of the tangent at the point (1/4, 1/4) of the ellipse \[\frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{12}=1\] is
A)
\[3x+y=48\] done
clear
B)
\[3x+y=3\] done
clear
C)
\[3x+y=16\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer81)
The angle between the pair of tangents drawn to the ellipse \[3{{x}^{2}}+2{{y}^{2}}=5\] from the point (1, 2), is [MNR 1984]
A)
\[{{\tan }^{-1}}\left( \frac{12}{5} \right)\] done
clear
B)
\[{{\tan }^{-1}}(6\sqrt{5})\] done
clear
C)
\[{{\tan }^{-1}}\left( \frac{12}{\sqrt{5}} \right)\] done
clear
D)
\[{{\tan }^{-1}}(12\sqrt{5})\] done
clear
View Solution play_arrow
-
question_answer82)
The equations of the tangents of the ellipse \[9{{x}^{2}}+16{{y}^{2}}=144\] which passes through the point (2, 3) is [MP PET 1996]
A)
\[y=3,\ x+y=5\] done
clear
B)
\[y=-3,\ x-y=5\] done
clear
C)
\[y=4,\ x+y=3\] done
clear
D)
\[y=-4,\ x-y=3\] done
clear
View Solution play_arrow
-
question_answer83)
If any tangent to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]cuts off intercepts of length h and k on the axes, then \[\frac{{{a}^{2}}}{{{h}^{2}}}+\frac{{{b}^{2}}}{{{k}^{2}}}=\]
A)
0 done
clear
B)
1 done
clear
C)
?1 done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer84)
If the line \[y=mx+c\]touches the ellipse \[\frac{{{x}^{2}}}{{{b}^{2}}}+\frac{{{y}^{2}}}{{{a}^{2}}}=1\], then \[c=\] [MNR 1975; MP PET 1994, 95, 99]
A)
\[\pm \sqrt{{{b}^{2}}{{m}^{2}}+{{a}^{2}}}\] done
clear
B)
\[\pm \sqrt{{{a}^{2}}{{m}^{2}}+{{b}^{2}}}\] done
clear
C)
\[\pm \sqrt{{{b}^{2}}{{m}^{2}}-{{a}^{2}}}\] done
clear
D)
\[\pm \sqrt{{{a}^{2}}{{m}^{2}}-{{b}^{2}}}\] done
clear
View Solution play_arrow
-
question_answer85)
The ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] and the straight line \[y=mx+c\] intersect in real points only if [MNR 1995]
A)
\[{{a}^{2}}{{m}^{2}}<{{c}^{2}}-{{b}^{2}}\] done
clear
B)
\[{{a}^{2}}{{m}^{2}}>{{c}^{2}}-{{b}^{2}}\] done
clear
C)
\[{{a}^{2}}{{m}^{2}}\ge {{c}^{2}}-{{b}^{2}}\] done
clear
D)
\[c\ge b\] done
clear
View Solution play_arrow
-
question_answer86)
If \[y=mx+c\] is tangent on the ellipse \[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{4}=1\], then the value of c is
A)
0 done
clear
B)
\[3/m\] done
clear
C)
\[\pm \sqrt{9{{m}^{2}}+4}\] done
clear
D)
\[\pm 3\sqrt{1+{{m}^{2}}}\] done
clear
View Solution play_arrow
-
question_answer87)
The locus of the point of intersection of the perpendicular tangents to the ellipse \[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{4}=1\] is [Karnataka CET 2003]
A)
\[{{x}^{2}}+{{y}^{2}}=9\] done
clear
B)
\[{{x}^{2}}+{{y}^{2}}=4\] done
clear
C)
\[{{x}^{2}}+{{y}^{2}}=13\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}=5\] done
clear
View Solution play_arrow
-
question_answer88)
The eccentric angles of the extremities of latus recta of the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] are given by
A)
\[{{\tan }^{-1}}\left( \pm \frac{ae}{b} \right)\] done
clear
B)
\[{{\tan }^{-1}}\left( \pm \frac{be}{a} \right)\] done
clear
C)
\[{{\tan }^{-1}}\left( \pm \frac{b}{ae} \right)\] done
clear
D)
\[{{\tan }^{-1}}\left( \pm \frac{a}{be} \right)\] done
clear
View Solution play_arrow
-
question_answer89)
Eccentric angle of a point on the ellipse \[{{x}^{2}}+3{{y}^{2}}=6\] at a distance 2 units from the centre of the ellipse is [WB JEE 1990]
A)
\[\frac{\pi }{4}\] done
clear
B)
\[\frac{\pi }{3}\] done
clear
C)
\[\frac{3\pi }{4}\] done
clear
D)
\[\frac{2\pi }{3}\] done
clear
View Solution play_arrow
-
question_answer90)
The equation of the tangents drawn at the ends of the major axis of the ellipse \[9{{x}^{2}}+5{{y}^{2}}-30y=0\], are [MP PET 1999]
A)
\[y=\pm 3\] done
clear
B)
\[x=\pm \sqrt{5}\] done
clear
C)
\[y=0,\ y=6\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer91)
The equation of the normal to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] at the point \[(a\cos \theta ,\ b\sin \theta )\] is
A)
\[\frac{ax}{\sin \theta }-\frac{by}{\cos \theta }={{a}^{2}}-{{b}^{2}}\] done
clear
B)
\[\frac{ax}{\sin \theta }-\frac{by}{\cos \theta }={{a}^{2}}+{{b}^{2}}\] done
clear
C)
\[\frac{ax}{\cos \theta }-\frac{by}{\sin \theta }={{a}^{2}}-{{b}^{2}}\] done
clear
D)
\[\frac{ax}{\cos \theta }-\frac{by}{\sin \theta }={{a}^{2}}+{{b}^{2}}\] done
clear
View Solution play_arrow
-
question_answer92)
If the normal at the point \[P(\theta )\] to the ellipse \[\frac{{{x}^{2}}}{14}+\frac{{{y}^{2}}}{5}=1\] intersects it again at the point \[Q(2\theta )\], then \[\cos \theta \] is equal to
A)
\[\frac{2}{3}\] done
clear
B)
\[-\frac{2}{3}\] done
clear
C)
\[\frac{3}{2}\] done
clear
D)
\[-\frac{3}{2}\] done
clear
View Solution play_arrow
-
question_answer93)
The line \[y=mx+c\]is a normal to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{a}^{2}}}=1\], if \[c=\]
A)
\[-(2am+b{{m}^{2}})\] done
clear
B)
\[\frac{({{a}^{2}}+{{b}^{2}})m}{\sqrt{{{a}^{2}}+{{b}^{2}}{{m}^{2}}}}\] done
clear
C)
\[-\frac{({{a}^{2}}-{{b}^{2}})m}{\sqrt{{{a}^{2}}+{{b}^{2}}{{m}^{2}}}}\] done
clear
D)
\[\frac{({{a}^{2}}-{{b}^{2}})m}{\sqrt{{{a}^{2}}+{{b}^{2}}}}\] done
clear
View Solution play_arrow
-
question_answer94)
The equation of normal at the point (0, 3) of the ellipse \[9{{x}^{2}}+5{{y}^{2}}=45\] is [MP PET 1998]
A)
\[y-3=0\] done
clear
B)
\[y+3=0\] done
clear
C)
x-axis done
clear
D)
y-axis done
clear
View Solution play_arrow
-
question_answer95)
The equation of the normal at the point (2, 3) on the ellipse \[9{{x}^{2}}+16{{y}^{2}}=180\], is [MP PET 2000]
A)
\[3y=8x-10\] done
clear
B)
\[3y-8x+7=0\] done
clear
C)
\[8y+3x+7=0\] done
clear
D)
\[3x+2y+7=0\] done
clear
View Solution play_arrow
-
question_answer96)
If the line \[x\cos \alpha +y\sin \alpha =p\] be normal to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\], then [MP PET 2001]
A)
\[{{p}^{2}}({{a}^{2}}{{\cos }^{2}}\alpha +{{b}^{2}}{{\sin }^{2}}\alpha )={{a}^{2}}-{{b}^{2}}\] done
clear
B)
\[{{p}^{2}}({{a}^{2}}{{\cos }^{2}}\alpha +{{b}^{2}}{{\sin }^{2}}\alpha )={{({{a}^{2}}-{{b}^{2}})}^{2}}\] done
clear
C)
\[{{p}^{2}}({{a}^{2}}{{\sec }^{2}}\alpha +{{b}^{2}}\text{cose}{{\text{c}}^{2}}\alpha )={{a}^{2}}-{{b}^{2}}\] done
clear
D)
\[{{p}^{2}}({{a}^{2}}{{\sec }^{2}}\alpha +{{b}^{2}}\text{cose}{{\text{c}}^{2}}\alpha )={{({{a}^{2}}-{{b}^{2}})}^{2}}\] done
clear
View Solution play_arrow
-
question_answer97)
The line \[lx+my+n=0\]is a normal to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\], if [DCE 2000]
A)
\[\frac{{{a}^{2}}}{{{m}^{2}}}+\frac{{{b}^{2}}}{{{l}^{2}}}=\frac{({{a}^{2}}-{{b}^{2}})}{{{n}^{2}}}\] done
clear
B)
\[\frac{{{a}^{2}}}{{{l}^{2}}}+\frac{{{b}^{2}}}{{{m}^{2}}}=\frac{{{({{a}^{2}}-{{b}^{2}})}^{2}}}{{{n}^{2}}}\] done
clear
C)
\[\frac{{{a}^{2}}}{{{l}^{2}}}-\frac{{{b}^{2}}}{{{m}^{2}}}=\frac{{{({{a}^{2}}-{{b}^{2}})}^{2}}}{{{n}^{2}}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer98)
The equation of tangent and normal at point (3, ?2) of ellipse \[4{{x}^{2}}+9{{y}^{2}}=36\] are [MP PET 2004]
A)
\[\frac{x}{3}-\frac{y}{2}=1,\ \frac{x}{2}+\frac{y}{3}=\frac{5}{6}\] done
clear
B)
\[\frac{x}{3}+\frac{y}{2}=1,\ \frac{x}{2}-\frac{y}{3}=\frac{5}{6}\] done
clear
C)
\[\frac{x}{2}+\frac{y}{3}=1,\ \frac{x}{3}-\frac{y}{2}=\frac{5}{6}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer99)
The value of \[\lambda \], for which the line \[2x-\frac{8}{3}\lambda y=-3\] is a normal to the conic \[{{x}^{2}}+\frac{{{y}^{2}}}{4}=1\] is [MP PET 2004]
A)
\[\frac{\sqrt{3}}{2}\] done
clear
B)
\[\frac{1}{2}\] done
clear
C)
\[-\frac{\sqrt{3}}{2}\] done
clear
D)
\[\frac{3}{8}\] done
clear
View Solution play_arrow
-
question_answer100)
The pole of the straight line \[x+4y=4\] with respect to ellipse \[{{x}^{2}}+4{{y}^{2}}=4\] is [EAMCET 2002]
A)
(1, 4) done
clear
B)
(1, 1) done
clear
C)
(4, 1) done
clear
D)
(4, 4) done
clear
View Solution play_arrow
-
question_answer101)
In the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\], the equation of diameter conjugate to the diameter \[y=\frac{b}{a}x\], is
A)
\[y=-\frac{b}{a}x\] done
clear
B)
\[y=-\frac{a}{b}x\] done
clear
C)
\[x=-\frac{b}{a}y\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer102)
An ellipse has OB as semi minor axis, F and F¢ its foci and the angle FBF¢ is a right angle. Then the eccentricity of the ellipse is [AIEEE 2005]
A)
\[\frac{1}{4}\] done
clear
B)
\[\frac{1}{\sqrt{3}}\] done
clear
C)
\[\frac{1}{\sqrt{2}}\] done
clear
D)
\[\frac{1}{2}\] done
clear
View Solution play_arrow
-
question_answer103)
If the foci of an ellipse are \[(\pm \sqrt{5},\,0)\] and its eccentricity is \[\frac{\sqrt{5}}{3}\], then the equation of the ellipse is [J & K 2005]
A)
\[9{{x}^{2}}+4{{y}^{2}}=36\] done
clear
B)
\[4{{x}^{2}}+9{{y}^{2}}=36\] done
clear
C)
\[36{{x}^{2}}+9{{y}^{2}}=4\] done
clear
D)
\[9{{x}^{2}}+36{{y}^{2}}=4\] done
clear
View Solution play_arrow
-
question_answer104)
The sum of the focal distances of any point on the conic \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\] is [Karnataka CET 2005]
A)
10 done
clear
B)
9 done
clear
C)
41 done
clear
D)
18 done
clear
View Solution play_arrow
-
question_answer105)
Minimum area of the triangle by any tangent to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] with the coordinate axes is [IIT Screening 2005]
A)
\[\frac{{{a}^{2}}+{{b}^{2}}}{2}\] done
clear
B)
\[\frac{{{(a+b)}^{2}}}{2}\] done
clear
C)
ab done
clear
D)
\[\frac{{{(a-b)}^{2}}}{2}\] done
clear
View Solution play_arrow
-
question_answer106)
The eccentricity of the ellipse \[25{{x}^{2}}+16{{y}^{2}}-150x-175=0\] is [Kerala (Engg.) 2005]
A)
2/5 done
clear
B)
2/3 done
clear
C)
4/5 done
clear
D)
3/4 done
clear
E)
3/5 done
clear
View Solution play_arrow
-
question_answer107)
The point (4, ?3) with respect to the ellipse \[4{{x}^{2}}+5{{y}^{2}}=1\] [Orissa JEE 2005]
A)
Lies on the curve done
clear
B)
Is inside the curve done
clear
C)
Is outside the curve done
clear
D)
Is focus of the curve done
clear
View Solution play_arrow
-
question_answer108)
A point ratio of whose distance from a fixed point and line \[x=9/2\] is always 2 : 3. Then locus of the point will be [DCE 2005]
A)
Hyperbola done
clear
B)
Ellipse done
clear
C)
Parabola done
clear
D)
Circle done
clear
View Solution play_arrow