If the equation of the circle cutting the circle x²+y²+2x-4y+8=0 orthogonally and coaxal with the circles x²+y²+6x+4y-12=0, x²+y²-4x-6y-12=0 is x²+y²+2ax+2by+c=0 then the ascending order of a, b, c is

The equation of the circle with centre at (2,3) and touching x-axis is

The condition that the circles x²+y²+2ax+2by+c=0, x²+y²+2bx+2ay+c=0 to touch each other is

The number of common tangents that can be drawn to the circles x²+y²=1 and  x²+y²-2x-6y+6=0 is

The lines 2x-3y=5 and 3x-4y=7 are two diameters of a circle of area 154 sq unit. Then the equation of this circle is

The circle x²+y²-4x+4y-1=0 cuts the positive coordinate axes in A and B respectively. The equation to the diameter of the circle perpendicular to the chord AB is

If the equation of the circle cutting orthogonally the circles x²+y²-6x=0, x²+y²+4x+3y+1=0 and which has its centre on the line x+2y=5 is x²+y²-2ax-2by+c=0 then the descending order of a, b, c is

The radius of the circle passing through the point (6, 2) and two of whose diameters are x+y=6 and x+2y=4 is

The locus of the midpoints of the chords of the circle 4x²+4y²-12x+4y+1=0 which subtend an angle of π/3 at its centre is a circle of radius

Let P be a point on the circle x²+y²=9, Q a point on the line 7x+y+3=0, and  the perpendicular bisector of PQ be the line x-y+1=0. Then the coordinates of P are