Solveeit Logo

Question

Question: The equation of the locus of the point of intersection of the perpendicular tangents to the ellipse ...

The equation of the locus of the point of intersection of the perpendicular tangents to the ellipse 9x2 + 16y2 = 144 is

A

x2 + y2 = 5

B

x2 + y2 = 7

C

x2 + y2 = 25

D

x2 + y2 = 2

Answer

x2 + y2 = 25

Explanation

Solution

The locus of point of intersection of perpendicular tangents to the ellipse is director circle x2+y2 = a2+2.

Given ellipse is x216+y29=1\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1

∓ Director circle equation is x2 + y2 =16 + 9 = 25