Applications Of Derivatives Question 176
Question: A point on the parabola $ y^{2}=18x $ at which the ordinate increases at twice the rate of the abscissa is
[AIEEE 2004]
Options:
A) $ ( \frac{9}{8},\frac{9}{2} ) $
B) (2, - 4)
C) $ ( \frac{-9}{8},\frac{9}{2} ) $
D) (2, 4)
Show Answer
Answer:
Correct Answer: A
Solution:
$ y^{2}=18x $ Differentiate both sides w.r.t. t $ 2y( \frac{dy}{dt} )=18( \frac{dx}{dt} ) $
therefore $ 2y( 2\frac{dx}{dt} )=18( \frac{dx}{dt} ) $ , $ ( \because \frac{dy}{dt}=2\frac{dx}{dt} ) $ \ $ 4y=18 $ or $ y=\frac{9}{2} $ and $ x=\frac{y^{2}}{18}=\frac{9}{8} $
Hence the required point is $ ( \frac{9}{8},\frac{9}{2} ) $ .
BETA
