Question

Number of points on the ellipse $\frac{x^2}{50}+\frac{y^2}{20}=1$ from which pair of perpendicular tangents are drawn to the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ is

• A. $0$
• B. $2$
• C. $1$
• D. $4$

Answer 1

The correct option is D $4$

For the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$, equation of

director circle is $x^2+y^2=25$. The director circle will cut the

ellipse $\frac{x^2}{50}+\frac{y^2}{20}=1$ at $4$ points

Hence, the number of points $=4$.