Question

Find the equation of the chord of contact of tangents from the point $(1,1)$ for the hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1.$

• A. $4x+9y=36$
• B. $9x+4y=36$
• C. $9x-4y=36$
• D. $4x-9y=36$

Answer 1

The correct option is D $4x-9y=36$

Given: Hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$, point $P(1,1)$

To Find: Equation of the chord of contact

Step - $1$: Recall formula of chord of contact
Step - $2$: Substitute values and simplify

We know that, the equation of the chord of contact of tangents to hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ from point $P(h,k)$ is given by $\frac{hx}{a^2}-\frac{ky}{b^2}=1.$

$\frac{1x}{9}-\frac{1y}{4}=1$

$\Rightarrow \frac{x}{9}-\frac{y}{4}=1$

$\Rightarrow 4x-9y=36$