Prove that the circle `x^2 + y^2 =a^2 and (x-2a)^2 + y^2 = a^2` are equal and touch each other. Also find the equation of a circle (or circles) of equal radius touching both the circles.

Prove that x^2+y^2=a^2 and (x-2a)^2+y^2=a^2 are two equal circles touching each other.

Show that the circles x^2 + y^2 + 2x-8y+8=0 and x^2 + y^2 + 10x - 2y+ 22=0 touch each other. Also obtain the equations of the two circles, each of radius 1, cutting both these circles orthogonally.

Find the equation of a circle with center (4,3) touching the circle x^(2)+y^(2)=1

Prove that the circle x^(2)+y^(2)+2x+2y+1=0 and circle x^(2)+y^(2)-4x-6y-3=0 touch each other.

If circles x^(2) + y^(2) = 9 " and " x^(2) + y^(2) + 2ax + 2y + 1 = 0 touch each other , then a =

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

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