Question

Number of points on the ellipse $\frac{x^{2}}{144}+\frac{y^{2}}{81}=1$ from which pair of perpendicular tangents are drawn to the ellipse $\frac{x^{2}}{64}+\frac{y^{2}}{36}=1$ is :-

Answer 1

We know, from any point on a director circle, perpendicular tangents can be drawn to the ellipse.
For ellipse $\frac{x^{2}}{64}+\frac{y^{2}}{36}=1$ , equation of director circle is $x^{2}+y^{2}=100$ .
This director circle will cut the ellipse $\frac{x^{2}}{144}+\frac{y^{2}}{81}=1$ at $4$ points.
Hence number of points $=4$