Show that the feet of the perpendiculars from the foci of the ellipse`x^2/a^2+y^2/b^2=1` on any of its tangents lie on its auxiliary circle

The product of the perpendiculars from the foci of the ellipse x^2/144+y^2/100=1 on any tangent is:

The product of the perpendiculars from the foci on any tengent to the ellipse x^2/a^2 + y^2/b^2 = 1 is

The product of the perpendiculars from the foci of the ellipse (x^(2))/(16)+(y^(2))/(4)=1 onto any tangent to the ellipse is

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 locus of the foot of the perpendicular drawn from the centre of the ellipse (x^(2))/( a^(2)) +(y^(2))/( b^(2)) =1 to any of its tangents is

The locus of foot of perpendicular from focus of ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 to its tangents is

The product of the perpendiculars from the foci on any tangent to the ellipse x^(2)//a^(2)+y^(2)//b^(2)=1 is