## Question

Five points are selected on a circle of radius a. the centers of the rectangular hyperbolas, each passing through four of these pints lie on a circle of a radius

### Solution

Let the circle be x^{2} + y^{2} = a^{2 }and 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

The equation of the line of latum of the rectangular hyperbola *xy* = *c*^{2} is

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

2*x – y* = 5 is

A straight line intersects the same branch of the hyperbola in P_{1} and P_{2} and meets its asymptotes in Q_{1} and Q_{2}. Then P_{1}Q_{2} – P_{2}Q_{1} is equal to

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 (*x*_{1}, *y*_{1}). Then is equal to

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

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

Sa circle with fixed center (3h, 3k) and of variable radius cuts the rectangular hyperbola x^{2} – y^{2} = 9a^{2} at the points A, B, C, D. The locus of the centroid of the triangle ABC is given by

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 –

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 subtends a right angle at the centre of the hyperbola then it always touches a fixed circle whose radius is –