Question

Find the length of tangent of $\frac{x^2}{9}-\frac{y^2}{9}=1$ at $(2,2)$.

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A $1$

Given the equation of hyperbola is

$\frac{x^2}{9}-\frac{y^2}{9}=1$ ............ $\left(1\right)$

Differentiating $\left(1\right)$ with respect to $x$ we get,

$2x-2y\frac{dy}{dx}=0$

$⟹2y\frac{dy}{dx}=2x$

$⟹\frac{dy}{dx}=\frac{x}{y}$ which gradient of hyperbola

$\therefore$ Length of tangent at $(2,2)$ is

${\left|\frac{dy}{dx}\right|}_{(2,2)}=\frac{2}{2}=1$

Therefore magnitude/length of tangent at $(2,2)$ is $1$.