Let two points P and Q lie on the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`,
whose centre C be such that CP is perpendicular to CQ,
a lt b. Then the value of `(1)/(CP^(2))+(1)/(CQ^(2))` is

For the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , let n be the number of points on the plane through which perpendicular tangents are drawn.

The locus of the poles of the chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 which subtend a right angle at its centre is

Prove that the locus of the middle-points of the chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 which pass through a fixed point (alpha, beta) is a hyperbola whose centre is ((alpha)/(2), (beta)/(2)) .

P is a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , and N is the foot of the perpendicular from P on the transverse axis. The tantent to the hyperbola at P meets the transverse axis at T. If O is the centre of the hyperbola, then OT.ON is equal to

Length of common tangents to the hyperbolas x^2/a^2-y^2/b^2=1 and y^2/a^2-x^2/b^2=1 is

If any tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 with centre C, meets its director circle in P and Q, show that CP and CQ are conjugate semi-diameters of the hyperbola.

Let P(6, 3) be a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1. If the normal at point P intersects the x-axis at (9, 0), then find the eccentricity of the hyperbola.

Let P(asectheta, btantheta) and A(asecphi, btanphi) , where theta+phi=(pi)/(2) , be two points on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . If (h, k) is the point of intersection of normals at P and Q. then k is equal to