If θ Is The Angle Between The Asymptotes Of The Hyperbola   with Eccentricity e, 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 number of tangents to the hyperbola  through (4, 3) 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 the two lines x – a = 0 and y – b =  0 are conjugate w.r.t. the hyperbolaxy = c², then the locus of (a, b) is

The equation of the tangents to the conic 3x² – y² = 3 perpendicular to the line x + 3y = 2 is

If P is a point on the hyperbola 16x² – 9y² = 144 whose foci are S₁ andS₂, then PS₁ – PS₂ =

The length of the transverse axis of a hyperbola is 7 and it passes through the point (5, –2). The equation of the hyperbola is

The locus of the point of intersection of the lines (x + y)t = a and x – y = at, where t is the parameter, is