P is any point of ellipse b2x2+a2y2=a2b2. Q is the foot of perpendicular from the centre to the tangent at P. As P moves around the ellipse,Q moves on the curve given by ----

x2 + y2 = a2

Eqn. of ellipse: x^2/a^2 + y^2/b^2=1

Eqn.of tangent at P: xcosΘ/a + ysinΘ/b=1

Eqn.of perpendicular from centre to tangent: y=(atanΘ/b)x

Coordinates of foot of  perpendicular Q (ab²cosΘ/a²sin²Θ+b²cos²Θ,a²bsinΘ/a²sin²Θ+b²cos²Θ)

Locus of Q: x²+y²=a²b²