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)`.

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 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 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)))

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))]

Product of lengths of perpendiculars drawn from the foci on any tangent to the hyperbola x^2/a^2-y^2/b^2=1 is :

The product of the perpendicular from the foci on any tangent to the hyperbola x^(2) //a^(2) -y^(2) //b^(2) =1 is

If the normal at a point P to the hyperbola x^2/a^2 - y^2/b^2 =1 meets the x-axis at G , show that the SG = eSP.S being the focus of the hyperbola.