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))]

If the normal at a pont 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.

The product of perpendicular drawn from any points on a hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 to its asymptotes is

If C is the centre of a hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , S, S its foci and P a point on it. Prove tha SP. S'P =CP^2-a^2+b^2

The tangent at the vertex of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets its conjugate hyperbola at the point whose coordinates are

The angle between a pair of tangents drawn from a point P to the hyperbola y^(2)=4ax is 45^(@) .Show that the locus of the point P is hyperbola.

Let P(4,3) be a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . If the normal at P intersects the x-axis at (16,0), then the eccentricity of the hyperbola is