Show that the product of the prependiculars from the foci and any tangent to an ellipse is equal to the square of the semi minor axis, and the feet of a these perpendiculars lie on the auxilary circle.

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

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

The distance between the foci of an ellipse is equal to half of its minor axis then eccentricity 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 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)

Find the equation of the curve in which the perpendicular from the origin on any tangent is equal to the abscissa of the point of contact.

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 SY and S'Y' be drawn perpendiculars from foci to any tangent to a hyperbola. Prove that y and Y' lie on the auxiliary circle and that product of these perpendicular is constant.