Show that the circles given by the following equation intersect each other orthogonally.
`x^2 + y^2 - 2x + 4y + 4 = 0,`
`x^2 + y^2 + 3x + 4y + 1 =0.`

Show that the circles given by the following equation intersect each other orthogonally. x^2 + y^2 - 2x - 2y - 7 = 0, 3x^2 + 3y^2 - 8x + 29y = 0 .

Show that the circles given by the following equations intersect each other orthogonally . x^2+y^2+2x-2y=0 x^2+y^2+2x + 2y=0

Show that the circles given by the following equations intersect each other orthogonally . x^2+y^2+4x-2y-11=0 x^2+y^2-4x-8y+11=0

Find the equation of the circle passing through the point of intersection of the circles x^2 + y^2 - 6x + 2y + 4 = 0, x^2 + y^2 + 2x - 4y -6 = 0 and with its centre on the line y = x.

Find the equation of the circle which passes through the origin and intersects each of the following circles orthogonally. x^2+y^2-4x-6y-3=0 x^2+y^2-8y+12=0

Show that the circles x^2 + y^2 - 2x-6y-12=0 and x^2 + y^2 + 6x+4y-6=0 cut each other orthogonally.

Find the parametric equation of the circles : x^2 + y^2 + 2x - 4y - 1 =0

Find the parametric equation of the circles : x^2 + y^2 - 2x+4y-4=0

Find the equation of the circle whose diameter is the common chord of the circles x^(2) + y^(2) + 2x + 3y + 1 = 0 and x^(2) + y^(2) + 4x + 3y + 2 = 0

The point of tangency of the circles x^2+ y^2 - 2x-4y = 0 and x^2 + y^2-8y -4 = 0 , is