If x²+y²+2gx+2fy+9=0 represents a circle with centre (1, -3) then radius=

The number of common tangents to the two circles x²+y²-8x+2y=0 and  x²+y²-2x-16y+25=0 is

From any point on the circle x²+y²=a² tangents are drawn to the circle x²+y²=a² sin²θ. The angle between them is

If the tangent at P on the circle x²+y²=a² cuts two parallel tangents of the circle at A and B then PA. PB=

If (1,2), (4, 3) are the limiting points of a coaxal system , then the equation of the circle in its conjugate system having minimum area is

If the lines 2x+3y+1=0, 3x+2y-1=0 intersect the coordinate axes in four concyclic points then the equation of the circle passing through these four points is

If the circles x²+y²=3a² , x²+y²-6x-8y+9=0 touch externally then a=

The equation to the circles whose radius is 3 and which touches internally the circle x²+y²-4x+6y-12=0 at he point (-1, 1) is

The equation of the chord of contact of the point (4, 2) with respect to the circle x²+y²-5x+4y-3=0 is

The two circles x²+y²=a², x²+y²=c²(c>0) touch each other if