Question

if an ellipse slides between two perpendicular straight lines, then the locus of its centre is

Answer 1

Consider the point of intersection of the perpendicular lines be the origin.

Let the center of the ellipse be (p,q).

Now,  the distance between the center of ellipse and such points is always given by $x^2+y^2$,

where 'x' and 'y' are the distances from the perpendicular lines.

Therefore, $x^2+y^2 = p^2 + q^2$

Hence, it represents the equation of circle.

Therefore, locus is found to be a part of the circle.