Question

An ellipse slides between two perpendicular straight lines. Then the locus of its centre is-

• A. A parabola
• B. An ellipse
• C. A circle
• D. A hyperbola

Answer 1

Answer: (C)

A circle

Answer 2

Since P is the point of intersection of two perpendicular tangents to the ellipse, P lies on the director circle. In the standard ellipse, the equation of the director circle is

x2 + y2 = a2 + b2.

Therefore CP2 = a2 + b2 whatever be the position of the ellipse.

\ locus of C is a circle