The product of the perpendiculars from the two foci of the ellipse `(x^(2))/(9)+(y^(2))/(25)=1` on the tangent at any point on the ellipse

If F_(1) and F_(2) are the feet of the perpendiculars from the foci S_(1)andS_(2) of the ellipse (x^(2))/(25)+(y^(2))/(16)=1 on the tangent at any point P on the ellipse,then prove that S_(1)F_(1)+S_(2)F_(2)>=8

The foci of the ellipse (x^(2))/(4) +(y^(2))/(25) = 1 are :

If M_(1) and M_(2) are the feet of perpendiculars from foci F_(1) and F_(2) of the ellipse (x^(2))/(64)+(y^(2))/(25)=1 on the tangent at any point P of the ellipse then

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

Let d_(1) and d_(2) be the lengths of perpendiculars drawn from foci S' and S of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 to the tangent at any point P to the ellipse. Then S'P : SP is equal to

Let d be the perpendicular distance from the centre of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 to the tangent drawn at a point P on the ellipse.If F_(1)&F_(2) are the two foci of the ellipse,then show the (PF_(1)-PF_(2))^(2)=4a^(2)[1-(b^(2))/(d^(2))]

The distance from the foci of P(a,b) on the ellipse (x^(2))/(9)+(y^(2))/(25)=1 are

The product of the perpendiculars drawn from the loci of the ellipse x^2/9+y^2/25=1 upon the tangent to it at the point (3/2, (5sqrt3)/2) is