The Number Of Tangents To The Hyperbola  through (4, 3) Is

PN is the ordinate of any point P on the hyperbola  and AA’ is its transverse axis. If Q divides AP in the ratio a² : b², then NQ is

If SK perpendicular from focus S on th tangent at any point P of the hyperbola  , then K lies on

The lines 2x + 3y + 4 = 0 and 3x – 2y + 5 = 0 may be conjugate w.r.t. the hyperbola  if

The condition for two diameters of a hyperbola  represented by Ax² + 2Hxy + By² = 0 to be conjugate is

If the polars of (x₁, y₁) and (x₂, y₂) w.r.t. the hyperbola  are at right angles, then 

The line 3x + 2y + 1 = 0 meets the hyperbola 4x² – y² = 4a² in the points P and Q. The coordinates of point intersection of the tangents at P and Qare

The eccentricity of the hyperbola whose latus rectum is half of its transverse axis is

The equation of the hyperbola referred to it axes as axes of coordinates whose latus rectum is 4 and eccentricity is 3, is

If a rectangular hyperbola whose center is C, is cut by any circle of radiusr in the four points P, Q, R, S, then 

CP² + CQ² + CR² + CS² =

If θ is the angle between the asymptotes of the hyperbola   with eccentricity e, then