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An ellipse slides between two perpendicu...

An ellipse slides between two perpendicular straight lines. Then identify the locus of its center.

A

parabola

B

ellipse

C

hyperbola

D

circle

Text Solution

Verified by Experts

The correct Answer is:
D
Clearly, P is the point of intersection of perpendicular tangents. So, P lies on the director circle of the given ellipse `x^(2)/a^(2) + y^(2)/b^(2) = 1` (say). This means that the centre of the ellipse will always remain at a constant distance `sqrt(a^(2) + b^(2))` from P. Hence, the locus of C is a circle.
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