The point on a circle nearest to the point `P(2,1)` is at a distance of 4 units and the farthest point is (6, 5). Then find the equation of the circle.

The normal at the point (3, 4) on a circle cuts the circle at the point (-1,-2). Then the equation of the circle is

The equation of radical axis of two circles is x + y = 1 . One of the circles has the ends ofa diameter at the points (1, -3) and (4, 1) and the other passes through the point (1, 2).Find the equating of these circles.

The line 2x-y+1=0 is tangent to the circle at the point (2, 5) and the center of the circle lies on x-2y=4 . Then find the radius of the circle.

A circle touches the y-axis at the point (0, 4) and cuts the x-axis in a chord of length 6 units. Then find the radius of the circle.

A tangent at a point on the circle x^2+y^2=a^2 intersects a concentric circle C at two points Pa n dQ . The tangents to the circle X at Pa n dQ meet at a point on the circle x^2+y^2=b^2dot Then the equation of the circle is

If the distance between the points (5,-2),(1,a) is 5 units . Find the value of a .

Circles are drawn through the point (2, 0) to cut intercept of length 5 units on the x-axis. If their centers lie in the first quadrant, then find their equation.

Two circles with equal radii are intersecting at the points (0, 1) and (0,-1). The tangent at the point (0,1) to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is.