Q. If $y = 4x - 5$ is tangent to the curve $y^{2} = px^{3} + q$ at (2, 3) then $(p,q)$ is
A) (2, 7)
B) $( - 2,\ 7)$
C) $( - 2,\ - 7)$
D) $(2,\ - 7)$
Explanation
(d)
Curve is $y^{2} = px^{3} + q$
$\therefore\ \ 2y\frac{dy}{dx} = 3px^{2}$
$\Rightarrow \ \ \left( \frac{dy}{dx} \right)_{(2,3)} = \frac{3p.4}{2.3}$
$\Rightarrow \ \ \ 4 = 2p$
$\Rightarrow \ \ \ p = 2$
Also, curve is passing through (2, 3)
$\therefore\ \ 9 = 8p + q$
$\Rightarrow \ \ \ q = - 7$
$\therefore(p,\ q)$ is $(2,\ - 7)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.