Question

The length of subtangent to the curve $x^{2}y^{2} = a^{4}$ at the point

$( - a,a)$ is

• A. $3a$
• B. $2a$
• C. a
• D. 4a

Answer 1

Answer: (C)

a

Answer 2

Equation of the curve $x^{2}y^{2} = a^{4}$.

Differentiating the given equation,

$x^{2}2y\frac{dy}{dx} + y^{2}2x = 0$ ⇒ $\frac{dy}{dx} = \frac{- y}{x}$ ⇒ $\left( \frac{dy}{dx} \right)_{( - a,a)} = - \left( \frac{a}{- a} \right) = 1$

Therefore, sub-tangent = $\frac{y}{\left( \frac{dy}{dx} \right)} = a$.