If the line 2x+3y+1=0 and 3x-y-4=0 lie along diameters of a circle of circumference 10π, then the equation of the circle is

The intercept made by the circle x²+y²-2hx sin θ-2ky sinθ=h² cos²θ on the x-axis is

The system of circle x²+y²+2λx-5=0 is

The equation of the tangent to the circle x²+y²-2x-4y+3=0 at (2, 3) is

The equation of the circle with centre (3, -2) and radius 3 is

The circles x²+y²-10x+16=0 and x²+y²=r² intersect each other into distinct points if

The centre of the circle passing through the points (0, 0), (1, 0) and touching the circle x²+y²=9 is

Consider the circle x²+y²-4x-2y+c=0 whose centre is A(2, 1). If the point P(10, 7) is such that the line segment PA meets the circle in Q with PQ=5, then c=

The points (2k, 3k), (1, 0), (0, 1) and (0, 0) lie on a circle for

The points A(2, 3) and B(-7, -12) are conjugate  points  w.r.  to the  circle x²+y²-6x- 8y- 1=0. The centre of the circle passing  through A and B and orthogonal to the given circle is