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 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

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

The equation of the line of latum of the rectangular hyperbola xy = c² is

The equation of normal to the rectangular hyperbola xy = 4 at the point P on the hyperbola which is parallel to the line

2x – y = 5 is