Question

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

Answer 1

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, number of points $=4$