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.

Examine whether the two circles x^2+y^2-2x-4y=0 and x^2+y^2-8y-4=0 touch each other externally or internally .

Two circles x^(2) + y^(2) -2kx = 0 and x^(2) + y^(2) - 4x + 8y + 16 = 0 touch each other externally.Then k is

Write the condition so that circles x^(2)+y^(2)+2ax+c=0 and x^(2)+y^(2)+2by+c=0 touch externally.

If circles (x -1)^(2) + y^(2) = a^(2) " and " (x + 2)^(2) + y^(2) = b^(2) touch each other externally , then

Show that the circles x ^(2) + y ^(2) - 2x =0 and x ^(2) + y ^(2) - 8x + 12=0 touch each other externally. Find the point of contact.

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