Question:
If $y=4x-5$ is tangent to the curve $y^{2}=px^{3}+q$ at $\left(\right.2, \, 3\left.\right)$ then $\left(\right.p,q\left.\right)$ is
If $y=4x-5$ is tangent to the curve $y^{2}=px^{3}+q$ at $\left(\right.2, \, 3\left.\right)$ then $\left(\right.p,q\left.\right)$ is
Updated On: Jul 28, 2022
- $\left(\right.2, \, 7\left.\right)$
- $\left(\right.-2, \, 7\left.\right)$
- $\left(\right.-2, \, -7\left.\right)$
- $\left(\right.2, \, -7\left.\right)$
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The Correct Option is D
Solution and Explanation
Curve is $y^{2}=px^{3}+q$
$\therefore \, \, 2y\frac{d y}{d x}=3px^{2}$
$\Rightarrow \, \, \left(\frac{d y}{d x}\right)_{\left(\right. 2,3 \left.\right)}=\frac{3 p . 4}{2.3}$
$\Rightarrow \, \, \, 4=2p$
$\Rightarrow \, \, \, p=2$
Also, curve is passing through $\left(\right.2, \, 3\left.\right)$
$\therefore \, \, 9=8p+q$
$\Rightarrow \, \, \, q=-7$
$? \, \, \left(p , \, q\right)$ is $\left(2 , \, - 7\right)$
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Concepts Used:
Application of Derivatives
Various Applications of Derivatives-
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