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]`.

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 ellipse. If F_(1) and F_(2) are the foci of the ellipse, then show that (PF_(1)-PF_(2))^(2)=4a^(2)(1-(b^(2))/(d^(2)))

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 p is the length of the perpendicular from the focus S of the ellipse x^(2)/a^(2)+y^(2)/b^(2) = 1 to a tangent at a point P on the ellipse, then (2a)/(SP)-1=

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

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

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

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

Show that the maximum distance of centre of the ellipse x^(2)/a^(2)+y^(2)/b^(2) = 1 from a normal to the ellipse is (a - b).