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

If x²+y²+6x+2ky+25=0 touches the y-axis then k=

Equation of the circle passing through (2, 0) and whose radical axis w. r. to the circle x²+y²=1 is at x=1/2 is

If the tangent from a point P to the circle x²+y²=1 is perpendicular to the tangent from P to the circle x²+y²=3, then the locus of P is

The locus of the poles of the line 2x-3y-4=0 w.r.t the circle x²+y²+2λx-16=0 is

Let AB be the chord 4x-3y +5 = 0 with respect to the circle x²+y²-2x+4y-20=0. If C= (7, 1), then the area of the triangle ABC is