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


Correct option is

 subtends a right angle at center i.e. (0, 0)

With the help of  and putting coefficient of x2 + coefficient of y = 0


‘p’ is also the length of perpendicular drawn from (0, 0) to the line , then radius of circle 



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


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

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


If values of m for which the line  touches the hyperbola 16x2 – 9y= 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 PQP’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


A straight line intersects the same branch of the hyperbola  in P1 and P2 and meets its asymptotes in Q1 and Q2. Then P1Q2 – P2Q1 is equal to