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

The circles x²+y²=1 ,  x²+y²+6x-2y=1 and x²+y²-12x+4y=1 are such that

The polar of the point (1, -2) w.r.t the circles  x²+y²+6y+5=0 , x²+y²+2x+8y+5=0 are

The number of common tangents to the two circles x²+y²=4, x²+y²-8x+12=0 is