Q. What is the slope of the tangent drawn to the hyperbola $xy = a,\ (a \neq 0)$ at the point $(a,\ 1)?$
A) $\frac{1}{a}$
B) $- \frac{1}{a}$
C) $a$
D) $- a$
Explanation
(b)
Given equation is $xy = a$
On differentiating, we get
$x\frac{dy}{dx} + y = 0$
$\Rightarrow \frac{dy}{dx} = - \frac{y}{x}$
$\Rightarrow \ \ \left( \frac{dy}{dx} \right)_{(a,1)} = - \frac{1}{a}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.