JEE Main & Advanced Mathematics Straight Line Question Bank

done Problems related to triangle and quadrilateral Locus Total Questions - 19

• question_answer1)
  If the extremities of the base of an isosceles triangle are the points \[(2a,0)\] and \[(0,a)\] and the equation of one of the sides is \[x=2a\], then the area of the triangle is
  A)
             \[5{{a}^{2}}sq\]. units               done clear
  B)
             \[\frac{5}{2}{{a}^{2}}sq.\]units done clear
  C)
             \[\frac{25{{a}^{2}}}{2}sq.\]units       done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer2)
  The equation to the sides of a triangle are \[x-3y=0\], \[4x+3y=5\] and \[3x+y=0\]. The line \[3x-4y=0\]passes through [EAMCET 1994]
  A)
             The incentre done clear
  B)
             The centroid done clear
  C)
             The circumcentre                       done clear
  D)
             The orthocentre of the triangle done clear
  View Solution play_arrow

• question_answer3)
  Area of the parallelogram formed by the lines \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\],\[{{a}_{1}}x+{{b}_{1}}y+{{d}_{1}}=0\]and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\], \[{{a}_{2}}x+{{b}_{2}}y+{{d}_{2}}=0\]is
  A)
             \[\frac{({{d}_{1}}-{{c}_{1}})({{d}_{2}}-{{c}_{2}})}{{{[(a_{1}^{2}+b_{1}^{2})(a_{2}^{2}+b_{2}^{2})]}^{1/2}}}\]         done clear
  B)
             \[\frac{({{d}_{1}}-{{c}_{1}})({{d}_{2}}-{{c}_{2}})}{{{a}_{1}}{{a}_{2}}-{{b}_{1}}{{b}_{2}}}\] done clear
  C)
             \[\frac{({{d}_{1}}+{{c}_{1}})({{d}_{2}}+{{c}_{2}})}{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}}\]       done clear
  D)
             \[\frac{({{d}_{1}}-{{c}_{1}})({{d}_{2}}-{{c}_{2}})}{{{a}_{1}}{{b}_{2}}-{{a}_{2}}{{b}_{1}}}\] done clear
  View Solution play_arrow

• question_answer4)
  Area of the parallelogram whose sides are \[x\cos \alpha +y\sin \alpha =p\] \[x\cos \alpha +y\sin \alpha =q,\,\,\] \[x\cos \beta +y\sin \beta =r\]  and \[x\cos \beta +y\sin \beta =s\] is
  A)
             \[\pm (p-q)(r-s)\,\text{cosec}(\alpha -\beta )\]                          done clear
  B)
             \[(p+q)(r-s)\,\text{cosec }(\alpha +\beta )\] done clear
  C)
             \[(p+q)(r+s)\,\text{cosec }(\alpha -\beta )\]                               done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer5)
  The area of the triangle bounded by the straight line \[ax+by+c=0,\,\,\,\,(a,b,c\ne 0)\] and the coordinate axes is        [AMU 2000]
  A)
             \[\frac{1}{2}\frac{{{a}^{2}}}{|bc|}\]                                            done clear
  B)
             \[\frac{1}{2}\frac{{{c}^{2}}}{|ab|}\] done clear
  C)
             \[\frac{1}{2}\frac{{{b}^{2}}}{|ac|}\]                                            done clear
  D)
             0 done clear
  View Solution play_arrow

• question_answer6)
  The triangle formed by the lines \[x+y-4=0,\,\] \[3x+y=4,\] \[x+3y=4\] is            [RPET 2002; IIT 1983; MNR 1992; UPSEAT 2001]
  A)
             Isosceles                                    done clear
  B)
             Equilateral done clear
  C)
             Right?angled                             done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer7)
  Two lines are drawn through (3, 4), each of which makes angle of 45o with the line \[x-y=2\], then area of the triangle formed by these lines is                          [RPET 2000]
  A)
             9      done clear
  B)
             9/2 done clear
  C)
             2      done clear
  D)
             2/9 done clear
  View Solution play_arrow

• question_answer8)
  The area of the triangle formed by the line \[x\sin \alpha +y\cos \alpha =\sin 2\alpha \]and the coordinates axes is
  A)
             \[\sin 2\alpha \]                        done clear
  B)
             \[\cos 2\alpha \] done clear
  C)
             \[2\sin 2\alpha \]                      done clear
  D)
             \[2\cos 2\alpha \] done clear
  View Solution play_arrow

• question_answer9)
  The area of a parallelogram formed by the lines \[ax\pm by\pm c=0\], is                                         [IIT 1973]
  A)
             \[\frac{{{c}^{2}}}{ab}\]              done clear
  B)
             \[\frac{2{{c}^{2}}}{ab}\] done clear
  C)
             \[\frac{{{c}^{2}}}{2ab}\]            done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer10)
  The triangle formed by \[{{x}^{2}}-9{{y}^{2}}=0\]and \[x=4\]is [Orissa JEE 2004]
  A)
             Isosceles                                    done clear
  B)
             Equilateral done clear
  C)
             Right angled                              done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer11)
  A point moves so that square of its distance from the point (3, -2) is numerically equal to its distance from the line \[5x-12y=13\]. The equation of the locus of the point is  [Roorkee 1974]
  A)
  \[13{{x}^{2}}+13{{y}^{2}}-83x+64y+182=0\] done clear
  B)
  \[{{x}^{2}}+{{y}^{2}}-11x+16y+26=0\] done clear
  C)
  \[{{x}^{2}}+{{y}^{2}}-11x+16y=0\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer12)
  Locus of the points which are at equal distance from \[3x+4y-11=0\]and \[12x+5y+2=0\]and which is near the origin is [MNR 1987]
  A)
             \[21x-77y+153=0\]                    done clear
  B)
             \[99x+77y-133=0\] done clear
  C)
             \[7x-11y=19\]                            done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer13)
  A point moves such that its distance from the point \[(4,\,0)\]is half that of its distance from the line \[x=16\]. The locus of this point is [AMU 1980]
  A)
             \[3{{x}^{2}}+4{{y}^{2}}=192\]    done clear
  B)
             \[4{{x}^{2}}+3{{y}^{2}}=192\] done clear
  C)
             \[{{x}^{2}}+{{y}^{2}}=192\]        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer14)
  The locus of a point so that sum of its distance from two given perpendicular lines is equal to 2 unit in first quadrant, is  [Bihar CEE 1994]
  A)
             \[x+y+2=0\]                                done clear
  B)
             \[x+y=2\] done clear
  C)
             \[x-y=2\]                                    done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer15)
  If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is [IIT 1992, Karnataka CET 1999; DCE 2000,01]
  A)
             Square                                        done clear
  B)
             Circle done clear
  C)
             Straight line                               done clear
  D)
             Two intersecting lines done clear
  View Solution play_arrow

• question_answer16)
  If a variable line drawn through the point of intersection of straight lines \[\frac{x}{\alpha }+\frac{y}{\beta }=1\]and \[\frac{x}{\beta }+\frac{y}{\alpha }=1\] meets the coordinate axes in A and B, then the locus of the mid point of \[AB\] is
  A)
             \[\alpha \beta (x+y)=xy(\alpha +\beta )\]                                   done clear
  B)
             \[\alpha \beta (x+y)=2xy(\alpha +\beta )\] done clear
  C)
             \[(\alpha +\beta )(x+y)=2\alpha \beta xy\]                                 done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer17)
  The point moves such that the area of the triangle formed by it with the points (1, 5) and (3, ?7) is 21sq. unit. The locus of the point is [Kerala (Engg.) 2002]
  A)
             \[6x+y-32=0\]                            done clear
  B)
             \[6x-y+32=0\] done clear
  C)
             \[x+6y-32=0\]                            done clear
  D)
             \[6x-y-32=0\] done clear
  View Solution play_arrow

• question_answer18)
  A straight line through the point (1, 1) meets the x-axis at 'A' and the y-axis at 'B'. The locus of the mid-point of AB is [UPSEAT 2004]
  A)
   \[2xy+x+y=0\]                            done clear
  B)
  \[x+y-2xy=0\] done clear
  C)
  \[x+y+2=0\]                            done clear
  D)
  \[x+y-2=0\] done clear
  View Solution play_arrow

• question_answer19)
  If A is (2, 5), B is (4, -11) and C lies on \[9x+7y+4=0\], then the locus of the centroid of the \[\Delta ABC\] is a straight line parallel to the straight line is                                                               [MP PET 1986]
  A)
  \[7x-9y+4=0\]                            done clear
  B)
  \[9x-7y-4=0\] done clear
  C)
  \[9x+7y+4=0\]                       done clear
  D)
  \[7+9y+4=0\] done clear
  View Solution play_arrow