Question

The locus of the point of intersection of the perpendicular tangents to the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$is

• A. $x^{2} + y^{2} = 9$
• B. $x^{2} + y^{2} = 4$
• C. $x^{2} + y^{2} = 13$
• D. $x^{2} + y^{2} = 5$

Answer 1

Answer: (C)

$x^{2} + y^{2} = 13$

Answer 2

The locus of point of intersection of two perpendicular tangents drawn on the ellipse is $x^{2} + y^{2} = a^{2} + b^{2},$ which is called “director circle”.

Given ellipse is $\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$.

**∴**Locus is $x^{2} + y^{2} = 9 + 4$, i.e. $x^{2} + y^{2} = 13$