Question

Tangents are drawn from any point on the circle $x^2+y^2=41$ to the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ then the angle between the two tangents is

• A. $\frac{\pi }{4}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{6}$
• D. $\frac{\pi }{2}$

Answer 1

Answer: (D)

$\frac{\pi }{2}$

$x^2+y^2=41=25+16$

$\therefore x^2+y^2=a^2+b^2$ is the director circle of

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Since director circle is the locus of intersection of perpendicular tangents.

$\therefore$ angle between the tangents is $\frac{\pi }{2}$