The longest distance from (-3, 2) to the circles x²+y²-2x+2y+1=0 is

If the equation of the circle passing through the origin and the points of intersection of the two circles x²+y²-4x-6y-3=0, x²+y²+4x-2y-4=0 is x²+y²+2ax+2by+c=0  then the ascending order of a, b,c is

The circle passing through the points (1, t), (t, 1) and (t, t) for all values of t passes through the point

The equation of the circle passing through the points of intersection of the circles x²+y²+2x+3y+1=0,  x²+y²+4x+3y+2=0 and through the point (-1, 2)is

The two circles x²+y²+2ax+2by+c=0 and x²+y²+2bx+2ay+c=0 have three real common tangents, then

The points (4, -2), (3, b) are conjugate w.r.t x²+y²=24 if b=

The equation of the common chord of the two circles (x-a)²+(y-b)²=c², (x-b)²+(y-a)²=c² is

The circumcircle of a triangle is given by x²+y²-4x+6y-3=0. The radius of the nine point circle of the triangle is

The line x cosα+y sinα=p touches the circle x²+y²-2axcosα-2aysinα=0, then p=

The locus of the centre of circle which touches the line x cos α+y sin α=p and circle (x-a)²+(y-b)²=c² is