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

The distance between the limiting points of the coaxial system x² + y² – 4x – 2y – 4 + 2λ(3x + 4y + 10)=0

If x²+y²-4x+6y+c=0 represents a circle radius 5 then c=

The equation of the circle cutting orthogonally the circles x²+y²-8x-2y+16=0, x²+y²-4x-4y-1=0 and passing through the point (1, 1) is

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