Conic Sections Question 392
Question: The point (4, -3) with respect to the ellipse $ 4x^{2}+5y^{2}=1 $
[Orissa JEE 2005]
Options:
A) Lies on the curve
B) Is inside the curve
C) Is outside the curve
D) Is focus of the curve
Show Answer
Answer:
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.
BETA
