Conic Sections Question 226
Question: The equation of normal at the point (0, 3) of the ellipse $ 9x^{2}+5y^{2}=45 $ is
[MP PET 1998]
Options:
A) $ y-3=0 $
B) $ y+3=0 $
C) x-axis
D) y-axis
Show Answer
Answer:
Correct Answer: D
Solution:
For $ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1, $ equation of normal at point $ (x_1,y_1) $ ,
therefore $ \frac{(x-x_1)a^{2}}{x_1}=\frac{(y-y_1)b^{2}}{y_1} $ ; $ (x_1,y_1)\equiv (0,3),a^{2}=5,b^{2}=9 $
$ \Rightarrow \frac{(x-0)}{0}5=\frac{(y-3).9}{3} $ or $ x=0 $ i.e., y-axis.
BETA
