Find the equation of the circle which passes through the origin and intersects the circles below, orthogonally.
`x^2 + y^2 - 4x + 6y + 10 = 0 `.
`x^2 + y^2 + 12y + 6 = 0 . `

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

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

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+10,x^(2)+y^(2)+12y+6=0

Find the equation of the circle which passes through the points of intersection of circles x^2 + y^2 - 2x - 6y + 6 = 0 and x^2 + y^2 + 2x – 6y + 6 = 0 and intersects the circle x^2 + y^2 + 4x + 6y +4=0 orthogonally.

Find the equation of the circle which passes through the point (2,0), (0,2) and orthogonally to the circle 2x^2 + 2y^2 + 5x - 6y + 4 = 0 .

Find the equation of the circle which passes through the points (2,0)(0,2) and orthogonal to the circle 2x^2+2y^2+5x-6y+4=0 .

Find the equation of the circle which passes through the points (2,0)(0,2) and orthogonal to the circle 2x^2+2y^2+5x-6y+4=0 .