Applications Of Derivatives Question 24
Question: The normal to the curve $ 2x^{2}+y^{2}=12 $ at the point (2, 2) cuts the curve again at
Options:
A) $ ( -\frac{22}{9},-\frac{2}{9} ) $
B) $ ( \frac{22}{9},\frac{2}{9} ) $
C) $ ( -,2,-2 ) $
D) none of these
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ 2x^{2}+y^{2}=12 $ or $ \frac{dy}{dx}=-\frac{2x}{y} $ . Slope of normal at point A (2, 2) is $ \frac{1}{2} $ . Also, point $ B( -\frac{22}{9},-\frac{2}{9} ) $ lies on the curve and slope of AB is $ \frac{2-(-2/9)}{2-(-22/9)}=\frac{1}{2} $
Hence, the normal meets the curve again at point $ ( -\frac{22}{9},-\frac{2}{9} ) $ .
BETA
