Prove that the product of the perpendicular from the foci on any tangent to an ellipse is equal to the square of the semi-minor axis.

Prove that the product of the perpendiculars from the foci upon any tangent to the ellipse x^2/a^2+y^2/b^2=1 is b^2

Prove that the product of the perpendiculars from the foci upon any tangent to the ellipse x^2/a^2+y^2/b^2=1 is b^2

Prove that the product of the perpendicular from the foci on any tangent to the ellips (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 is equal to b^(2)

The product of the perpendiculars drawn from the two foci of an ellipse to the tangent at any point of the ellipse is

Let S=(3,4) and S'=(9,12) be two foci of an ellipse. If the coordinates of the foot of the perpendicular from focus S to a tangent of the ellipse is (1, -4) then the eccentricity of the ellipse is

The locus of the foot of the perpendicular from the foci an any tangent to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , is

Prove that in an ellipse, the perpendicular from a focus upon any tangent and the line joining the centre of the ellipse to the point of contact meet on the corresponding directrix.

Prove that perpendicular drawn from focus upon any tangent of a parabola lies on the tangent at the vertex

Statement 1 : For the ellipse (x^2)/5+(y^2)/3=1 , the product of the perpendiculars drawn from the foci on any tangent is 3. Statement 2 : For the ellipse (x^2)/5+(y^2)/3=1 , the foot of the perpendiculars drawn from the foci on any tangent lies on the circle x^2+y^2=5 which is an auxiliary circle of the ellipse.

If two points are taken on the minor axis of an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 at the same distance from the center as the foci, then prove that the sum of the squares of the perpendicular distances from these points on any tangent to the ellipse is 2a^2dot