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

If the of the circle passing through the points (3,4),(3,2),(1,4) is x²+y²+2ax+2by+c=0, then the ascending order of a, b, c is

(1, 2) is a point on the circle x²+y²+2x-6y+5=0 which is orthogonal to x²+y²=5. The  conjugate  point  of (1, 2) w. r. to the circle x²+y² =5 and which lies on the first circle is

Let C₁=x²+y²-2x-4y=0, C₂=x²+y²+2x+10y=0 and L=2x+7y+7=0 Then L is the