A) Lies on the curve
B) Is inside the curve
C) Is outside the curve
D) Is focus of the curve
Correct Answer: C
Solution :
Using the condition the point \[({{x}_{1}},\,{{y}_{1}})\] lies (i) On the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}-1=0\] if \[\frac{x_{1}^{2}}{{{a}^{2}}}+\frac{y_{1}^{2}}{{{b}^{2}}}-1=0\] (ii) Outside the ellipse if \[\frac{x_{1}^{2}}{{{a}^{2}}}+\frac{y_{1}^{2}}{{{b}^{2}}}-1>0\] (iii) Inside the ellipse if \[\frac{x_{1}^{2}}{{{a}^{2}}}+\frac{y_{1}^{2}}{{{b}^{2}}}-1<0\] Given ellipse is \[\frac{{{x}^{2}}}{1/4}+\frac{{{y}^{2}}}{1/5}=1\] \ \[\frac{16}{1/4}+\frac{9}{1/5}-1=64+45-1>0\] Point (4, ?3) lies outside the ellipse.
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