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.

If the normal at 'theta' on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets the transverse axis at G , and A and A' are the vertices of the hyperbola , then AC.A'G=

If the normal at P to the rectangular hyperbola x^(2) - y^(2) = 4 meets the axes of x and y in G and g respectively and C is the centre of the hyperbola, then 2PC =

If the tangents at the point (a sec alpha, b tan alpha) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets the transverse axis at T , then the distance of T from a focus of the hyperbola, is

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).

If the tangent at the point (asec alpha, b tanalpha ) to the hyberbola (x^(2))/(a^(2)) -(y^(2))/(b^(2)) =1 meets the transverse axis at T. Then the distances of T form a focus of the hyperbola is

The normal at a point P on the parabola y^^2= 4ax meets the X axis in G.Show that P and G are equidistant from focus.

[" 18.If the normal at " t_(1) " on the hyperbola " xy=c^(2) " meets the hyperbola at t_(2) then

If the normal at P(theta) on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 with focus S ,meets the major axis in G. then SG=