Question

An ellipse whose axes are of length $2a$ and $2b$ slides between two lines at right angles to one another. The locus of its centre is

• A. $x^2+y^2=a^2-b^2$
• B. $x^2+y^2=a^2+b^2$
• C. $x^2-y^2=a^2+b^2$
• D. $x^2-y^2=a+b$

Answer 1

The correct option is B $x^2+y^2=a^2+b^2$

The 2 perpendicular lines touch the ellipse and so P,

their point of intersection,

lies on the director circle whose centre C is the centre of the ellipse,

and whose radius is,

$\sqrt{a^2+b^2}$.

$\therefore CP=\sqrt{a^2+b^2}=$ constant

But P is fixed, hence C lies on a circle, centre P and radius $\sqrt{a^2+b^2}$.