Question

If tangents are drawn from any point on the circle $x^2+y^2=25$ to the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1,$ then the angle between the tangents is

• A. $\frac{2\pi }{3}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{2}$

Answer 1

The correct option is D $\frac{\pi }{2}$

The locus of the point of intersection of the tangents to the ellipse which meet at right angle, is a circle. This circle is called the "director circle" of the ellipse.

Since $x^2+y^2=a^2+b^2$ is the director circle of the ellipse, which turns out to be the given circle.

The angle between tangents would be $\frac{\pi }{2}.$