Question

Solution

Correct option is Let the circle be x2 + y2 = aand let the centers of a rectangular hyperbola be (h, k). Let the given points on the circle be , I = 1, 2, 3, …. , so that  Similarly,  .

Since the points are given, L and M are known.    .

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

From a point on the line y = x + c, c (parameter), tangents are drawn to the hyperbola such that chords of contact pass through a fixed point (x1y1). Then is equal to

Q5

If the portion of the asymptotes between center and the tangent at the vertex of hyperbola in the third quadrant is cut by the line being parameter, then

Q6

A, B, C and D are the points of intersection of a circle and a rectangular hyperbola which have different centers. If AB passes through the center of the hyperbola, then CD passes through

Q7

Sa circle with fixed center (3h, 3k) and of variable radius cuts the rectangular hyperbola x2 – y2 = 9a2 at the points A, B, C, D. The locus of the centroid of the triangle ABC is given by

Q8

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

Q9

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 –

Q10

If a variable line which is a chord of the hyperbola subtends a right angle at the centre of the hyperbola then it always touches a fixed circle whose radius is –