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

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 

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

Portion of asymptote of hyperbola  (between center and the tangent at vertex) in the first quadrant is cut by the line

y + λ (x – a) = 0 (λ is a parameter) then

If a variable line , which is a chord of the hyperbola  (b > a), subtends a right angle at the centre of the hyperbola then it always touches a fixed circle whose radius is

If values of m for which the line  touches the hyperbola 16x² – 9y² = 144 are the roots of the equation 

x² – (a + b)x – 4 = 0, then value of (a, b) is equal to

Let any double ordinate PNP’ of the hyperbola  be produced both sides to meet the asymptotes in Q and Q’, then PQ. P’Q is equal to