Question

Find the equation of the chord of contact of tangents from the point $(2,3)$ to the hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$.

• A. $8x-27y=-36$
• B. $8x+7y=36$
• C. $8x-27y=36$
• D. $4x-27y=36$

Answer 1

The correct option is C $8x-27y=36$

Given: Hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$, point $(2,3)$

To Find: Equation of the chord of contact

We know that, the equation of the chord of contact is given by $\frac{hx}{a^2}-\frac{ky}{b^2}=1.$

From the given data, we have, $h=2,k=3,a^2=9,b^2=4$

Substituting all these values in the equation of chord of contact.
$\frac{2x}{9}-\frac{3y}{4}=1$

$\Rightarrow \frac{8x-27y}{36}=1$

$\Rightarrow 8x-27y=36$