Question

If the locus of the point of intersection of perpendicular tangents to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is a circle with centre at $(0,0)$, then the radius of the circle would be

• A. $a+b$
• B. $ab$
• C. $\frac{b}{a}$
• D. $\sqrt{(a^2+b^2)}$

Answer 1

The correct option is D $\sqrt{(a^2+b^2)}$

Such a circle is called director circle whose equation is given by $x^2+y^2=a^2+b^2$

$\Rightarrow r=\sqrt{a^2+b^2}$.