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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.

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Ellipse slides between two perpendicular lines. So, these lines are perpendicular tangents and their point of intersection P lies on the director circle.
If centre of the ellipse is fixed, then all the points of intersection of perpendicular tangents lie at at fixed distance which is equal to radius of the director circle.
So, if point of intersection of perpendicular tangents is fixed (point P,) then centre of variable ellipe also lies at fixed distance from point P.
Therefore, locus of centre of the ellipse is a circle.
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