Examine whether the circles x`^2` + y `^2` - 2x - 4y = 0 and x`^2` + y`^2` - 8y - 4 = 0 touch each other.

If the circles x ^2 + y ^2 + 2ax + c = 0 and x ^2 + y ^2 +2by + c = 0 touch each other, prove that 1/a ^2 + 1 b ^2 = 1/c

A circle passes through the point of intersection of the circles x ^2 + y ^2 + 13x - 3y = 0 and 2x ^2 + 2y ^2 + 4x - 7y - 25 = 0 and also through the point (1, 1). Find its equation.

Find the equation of the tangents to the circle x ^2 + y ^2 - 2x - 4y - 4 = 0 which are perpendicular to the line 3x - 4y - 1 = 0

Without solving the equations show that the straight lines 4x - y + 2 = 0, 3x + 2y -1 = 0 and x - 3y + 3 = 0 are concurrent.

Find the equation of the circle concentric with the circle x ^2 + y ^2 - 8x + 12y + 15 = 0 and passing through the point (5, 4).

Find the equation of the diameter of the circle x ^2 + y ^2 - 14x + 6y + 9 = 0 which passes through the point (2, 1).

Find the centre and radius of the circle x^2+y^2+8x+10y-8=0 .

Which of the following equation represent circles? (iii) x ^2 + y ^2 + 2x + 4y + 6xy + 8 = 0

Determine the centre and the radius if the circle x^2+y^2-8x+10y-12=0