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 y-axis at (0, 5) and whose centre lies on the line 2x + y = 13, find the equation of the circle.

If the lines 3x-4y+4=0 and 6x-8y-7=0 are tangents to a circle, then find the radius of the circle.

3x + y = 5 and x+y+1 = 0 are two diameters to the circle which passes through the point (-2, 2). Find its equation. Also find the radius of the circle.

If one end of the diameter is (1, 1) and the other end lies on the line x+y=3 , then find the locus of the center 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 (a) x^2+y^2=a b (b) x^2+y^2=(a-b)^2 (c) x^2+y^2=(a+b)^2 (d) x^2+y^2=a^2+b^2

If one of the diameters of the circle x^2+y^2-2x-6y+6=0 is a chord to the circle with centre (2,1), then the radius of the circle is

Find the equation of the circle passes through the points (4,3) and (-2 , 5) and whose centre lies on the line 2x - 3y = 4

A circle passes through(1,-2) and (4,-3) and its.centre lies on the straight line 3x + 4y= 7. Find the equation of the circle.-

Find the equation of the circle which passes through the points (3,-2)a n d(-2,0) and the center lies on the line 2x-y=3