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 16x2ā+9y2ā=1
ā“ Director circle equation is x2 + y2 =16 + 9 = 25