Prove that the circles `x^2+y^2+24ux+2vy=0` and `x^2+y^2+2u_1x+2v_1y=0` touch each other externally if `-12u_1u=v_1v`.

The circles x^(2)+y^(2)+2x-2y+1=0 and x^(2)+y^(2)-2x-2y+1=0 touch each other

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.

The circles x^2 + y^2 + 2ux + 2vy = 0 and x^2 + y^2 + 2u_1 x + 2v_1 y = 0 touch each other at (1, 1) if : (A) u + u_1 = v + v_1 (B) u + v = v_1 + u_1 (C) u/u_1 = v/v_1 (D) none of these

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 .

Prove that the curves y^2=4x and x^2+y^2-6x+1=0 touch each other at the points (1,\ 2) .

Prove that the curves y^2=4x and x^2+y^2-6x+1=0 touch each other at the points (1,\ 2) .

The point at which the circles x^(2)+y^(2)-4x-4y+7=0 and x^(2)+y^(2)-12x-10y+45=0 touch each other is

Prove that the circle x^(2) + y^(2) + 2ax + c^(2) = 0 and x^(2) + y^(2) + 2by + c^(2) = 0 touch each other if (1)/(a^(2)) + (1)/(b^(2)) = (1)/(c^(2)) .

Prove that the circles x^(2) +y^(2) - 4x + 6y + 8 = 0 and x^(2) + y^(2) - 10x - 6y + 14 = 0 touch at the point (3,-1)

If circles x^(2) + y^(2) + 2g_(1)x + 2f_(1)y = 0 and x^(2) + y^(2) + 2g_(2)x + 2f_(2)y = 0 touch each other, then