Find the number of points on ellipse $\frac{x^2}{50}+\frac{y^2}{20}=1$ from which pair of perpendicular tangents are drawn to ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$
Normal from a point $(5\sqrt{2}cos\theta, 2\sqrt{5} sin\theta)$ from which normal can be drawn on ellipse $\frac{x^2}{50}+\frac{y^2}{20}=1$
Equation of a normal can be written as $$\frac{5\sqrt{2}x}{cos\theta}-\frac{2\sqrt{5}y}{sin\theta}=30 $$ [By using $\frac{ax}{cos\theta}-\frac{by}{sin\theta}=a^2-b^2$] please suggest further how to approach in such problem thanks.
