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

If two points P & Q on the hyperbola , x^2/a^2-y^2/b^2=1 whose centre is C be such that CP is perpendicularal to CQ and a lt b 1 ,then prove that 1/(CP^2)+1/(CQ^2)=1/a^2-1/b^2 .

The slope of the tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point ( x_(1),y_(1)) is-

If e_1 is the eccentricity of the hyperbola (y^(2))/(b^(2)) - (x^(2))/(a^(2)) = 1 then e_(1) =

If the tangent at point P(h, k) on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 cuts the circle x^(2)+y^(2)=a^(2) at points Q(x_(1),y_(1)) and R(x_(2),y_(2)) , then the vlaue of (1)/(y_(1))+(1)/(y_(2)) is

Let P(a sec theta , b tan theta ) and Q(a sec phi , b tan phi) where theta + phi = (pi)/(2) be two point on the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) =1 .If ( h, k) be the point of intersection of the normals at P and Q , then the value of k is -

Let P b any point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 whose ordinate is PN. AA′ is its transverse axis. If the point Q divides AP in the ratio a^(2):b^(2) , then NQ is?

Let the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 be reciprocal to that of the ellipse x^(2)+9y^(2)=9 , then the ratio a^(2):b^(2) equals

Show that the midpoints of focal chords of a hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 lie on another similar hyperbola.

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 tangent 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

For 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.