Applications Of Derivatives Question 221
Question: If $ y=4x-5 $ is tangent to the curve $ y^{2}=px^{3}+q $ at (2, 3), then
[IIT 1994; UPSEAT 2001]
Options:
A) $ p=2,q=-7 $
B) $ p=-2,q=7 $
C) $ p=-2,q=-7 $
D) $ p=2,q=7 $
Show Answer
Answer:
Correct Answer: A
Solution:
Given curve $ y^{2}=px^{3}+q $ …………..(i)
Differentiate with respect to x, $ 2y.\frac{dy}{dx}=3px^{2} $
therefore $ \frac{dy}{dx}=\frac{3p}{2}( \frac{x^{2}}{y} ) $
$ \therefore {{| \frac{dy}{dx} |} _{2,3}}=\frac{3p}{2}\times \frac{4}{3}=2p $
For given line, slope of tangent $ =4 $
$ \therefore 2p=4 $
therefore $ p=2 $
From equation (i), $ 9=2\times 8+q $
therefore $ q=-7 $ .
BETA
