Conic Sections Question 280
Question: The equation of tangent and normal at point (3, -2) of ellipse $ 4x^{2}+9y^{2}=36 $ are
[MP PET 2004]
Options:
A) $ \frac{x}{3}-\frac{y}{2}=1,\ \frac{x}{2}+\frac{y}{3}=\frac{5}{6} $
B) $ \frac{x}{3}+\frac{y}{2}=1,\ \frac{x}{2}-\frac{y}{3}=\frac{5}{6} $
C) $ \frac{x}{2}+\frac{y}{3}=1,\ \frac{x}{3}-\frac{y}{2}=\frac{5}{6} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Given, equation of ellipse is $ 4x^{2}+9y^{2}=36 $
Tangent at point (3,-2) is $ \frac{(3)x}{9}+\frac{(-2)y}{4}=1 $ or $ \frac{x}{3}-\frac{y}{2}=1 $
$ \therefore $ Normal is $ \frac{x}{2}+\frac{y}{3}=k $ and it passes through point (3,-2)
$ \therefore $ $ \frac{3}{2}-\frac{2}{3}=k\Rightarrow k=\frac{5}{6} $
$ \therefore $ Normal is, $ \frac{x}{2}+\frac{y}{3}=\frac{5}{6} $ .
BETA
