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 'p' be the perpendicular distance from the centre C of the hyperbola x^2/a^2-y^2/b^2=1 to the tangent drawn at a point R on the hyperbola. If S & S' are the two foci of the hyperbola, then show that (RS + RS')^2 = 4 a^2(1+b^2/p^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

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

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=

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

Number of points on the ellipse x^2/a^2+y^2/b^2=1 at which the normal to the ellipse passes through at least one of the foci of the ellipse is

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

Let P be a point on the ellipse x^2/100 + y^2/25 =1 and the length of perpendicular from centre of the ellipse to the tangent to ellipse at P be 5sqrt(2) and F_1 and F_2 be the foci of the ellipse, then PF_1.PF_2 .

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