Find the condition if the circle whose equations are `x^2+y^2+c^2=2a x` and `x^2+y^2+c^2-2b y=0` touch one another externally.

If the circles x^2 + y^2 + 2ax + b = 0 and x^2+ y^2+ 2cx + b = 0 touch each other (a!=c)

Find the equation of the straight lines touching both x^2+y^2=2a^2 and y^2=8a xdot

Find the coordinates of the point at which the circles x^2-y^2-4x-2y+4=0 and x^2+y^2-12 x-8y+36=0 touch each other. Also, find equations of common tangents touching the circles the distinct points.

The radius of the circle whose two normals are represented by the equation x^2-5 x y-5 x+25 y=0 and which touches externally the circle x^2+y^2-2 x+4 y-4 =0 is equal to

Find the equation of the family of circles touching the lines x^2-y^2+2y-1=0.

Find the equations to the common tangents of the circles x^2+y^2-2x-6y+9=0 and x^2+y^2+6x-2y+1=0

Find the length of the common chord of the circles x^2+y^2+2x+6y=0 and x^2+y^2-4x-2y-6=0

If two circles x^(2)+y^(2)+c^(2)=2ax and x^(2)+y^(2)+c^(2)-2by=0 touch each other externally , then prove that (1)/(a^(2))+(1)/(b^(2))=(1)/(c^(2))

The centre of the smallest circle touching the circles x^2+ y^2-2y -3=0 and x^2 +y^ 2-8x -18y +93= 0 is:

There are two circles whose equation are x^2+y^2=9 and x^2+y^2-8x-6y+n^2=0,n in Zdot If the two circles have exactly two common tangents, then the number of possible values of n is 2 (b) 8 (c) 9 (d) none of these