Question

Find the equation of chord of contact of tangents drawn from a point $(5,5)$ to the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$

• A. None of the above
• B. $\frac{x}{9}+\frac{y}{4}=1$
• C. $\frac{x}{9}+\frac{y}{4}=4$
• D. $\frac{x}{9}+\frac{y}{4}=\frac{1}{5}$

Answer 1

The correct option is D $\frac{x}{9}+\frac{y}{4}=\frac{1}{5}$

We have, an ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ and a external point $(5,5)$

We know, equation of chord of contact of tangents to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ drawn from $P(h,k)$ is, $\frac{hx}{a^2}+\frac{ky}{b^2}=1$

$\text{Here,}{a}^2=9,b^2=4,h=k=5$
Substituting the values, we get,
$\frac{5x}{9}+\frac{5y}{4}=1$
$\Rightarrow \frac{x}{9}+\frac{y}{4}=\frac{1}{5}$
This is the required equation