The equation of the circle whose centre lies in the first quadrant and which touches the coordinate axes and the line (x/3)+(y/4)=1 is x²+y²-2cx-2cy+c²=0, then c=

The equation to the locus of the midpoints of chords of the circle x2+y2-8x+6y+20=0 which are parallel to 3x + 4y+5 = 0 is

The radical centre of the circle x²+y²=1, x²+y²-2x=1, x²+y²-2y=1 is

The length of the common chord of the circles x²+y²+2hx=0, x²+y²-2ky=0 is

If the pole of a line w.r.to the circle x²+y²=a² lies on the circle x²+y²=a⁴ then the line touches the circle

Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the midpoints of the chords of the circle C that subtend an angle of 2π/3 at its centre is

The equations of the tangents to the circle x²+y²+8x-4y-5=0 and perpendicular to 2x+3y+5=0 are

For the circle2x²+2y²-5x-4y-3=0, the point (4, 2)

If the lines 2x+y+12=0, kx-3y-10=0 are conjugate w.r.t the circle x²+y²-4x+3y-1=0, then k=

Equation of the circle touching the y-axis at (0, √3) and cuts the x-axis in the points (- 1, 0) and (-3, 0) is