Question

Find the equation of chord of contact to the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ at the point $(1,3).$

• A. $\frac{y}{16}+\frac{x}{3}=1$
• B. $\frac{y}{16}-\frac{x}{3}=1$
• C. $\frac{x}{16}+\frac{y}{3}=1$
• D. $\frac{x}{16}-\frac{y}{3}=1$

Answer 1

The correct option is C $\frac{x}{16}+\frac{y}{3}=1$

The equation of chord of contact for the ellipse $\frac{x^2}{19}+\frac{y^2}{9}=1$ is given by
$\frac{x{x}_1}{16}+\frac{y{y}_1}{9}=1$ where $(x_1,y_1)$ is the point of contact.
Substituting $(x_1,y_1)=(1,3)$ gives us
$\frac{x}{16}+\frac{3y}{9}=1$
Or
$\frac{x}{16}+\frac{y}{3}=1$