Applications Of Derivatives Question 268
Question: A point on the parabola $ y^{2}=18x $ at which the ordinate increases at twice the rate of the abscissa is
Options:
A) (2, 4)
B) (2, -4)
C) $ ( \frac{-9}{8},\frac{9}{2} ) $
D) $ ( \frac{9}{8},\frac{9}{2} ) $
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Answer:
Correct Answer: D
Solution:
[d] The equation of the parabola is $ y^{2}=18x $ . Differentiating w.r.t. t, we get $ 2y\frac{dy}{dt}=18\frac{dx}{dt} $
$ \Rightarrow 2\times 2y=18 $
$ ( \therefore \frac{dy}{dt}=2\frac{dx}{dt} ) $
$ \Rightarrow y=\frac{9}{2} $ From the equation of the parabola, we get $ {{( \frac{9}{2} )}^{2}}=18x $
$ \Rightarrow \frac{81}{4}=18x $
$ \Rightarrow x=\frac{81}{4\times 18} $
$ \Rightarrow x=\frac{9}{8} $
Hence, the point is $ (9\text{/}8,,9\text{/}2) $ .
BETA
