Conic Sections Question 239
Question: The equation of the normal at the point (2, 3) on the ellipse $ 9x^{2}+16y^{2}=180 $ , is
[MP PET 2000]
Options:
A) $ 3y=8x-10 $
B) $ 3y-8x+7=0 $
C) $ 8y+3x+7=0 $
D) $ 3x+2y+7=0 $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{x-x_1}{x_1/a^{2}}=\frac{y-y_1}{y_1/b^{2}} $ , which is the standard equation of normal at point $ (x_1,y_1) $ . In the given ellipse, $ a^{2}=20,b^{2}=\frac{180}{16} $ .
Hence the equation of normal at the point $ (2,3) $ is $ \frac{x-2}{2/20}=\frac{y-3}{48/180} $
therefore $ 40(x-2)=15(y-3) $
therefore $ 8x-3y=7 $
therefore $ 3y-8x+7=0 $ .
BETA
