The equation of the circle which cuts orthogonally the  three circles x²+y²+2x+17y+4=0, x²+y²+7x+6y+11=0 , x²+y²-x+22y+3=0 is

If a chord of the circle x²+y²=8 makes equal intercepts of length a on the coordinate axes, then |a|<

I:The equation whose roots are the squares of the roots of x³-x²+8x-6=0 is x³+15x²+52x+36=0

II:The equation whose roots are the cubes of the roots x³+3x²+2=0 is x³+33x²+12x+8=0

If the circles x²+y²+2ax+4ay-3a²=0 and x²+y²-8ax-6ay+7a²=0 touch each other externally, the point of contact is

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