The Equation Of The Tangents To The Conic 3x2 – y2 = 3 Perpendicular To The Line x + 3y = 2 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 

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

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 

If PQ is a double ordinate of the hyperbola  such that OPQ is an equilateral triangle, O being the center of the hyperbola. Then the eccentricity e of the hyperbola satisfies

A rectangular hyperbola passes through the points A(1, 1), B(1, 5), and C(3, 1). The equation of normal to the hyperbola at A(1, 1) is