Two circles have equations
x^2 + y^2 + 2ax + 2by + c = 0
x^2 + y^2 + 2a'x + 2b'y + c' = 0
Show that these circles are orthogonal if 2aa' + 2bb' = c + c'
I'm assuming you have to grad both of these to get an expression for the vector normal to the tangent at any point on each circle. However I am unsure of how to finish - I thought of dot producting them and setting this to zero, but would this be correct, as this would mean the radii/tangents are perpendicular no matter which points they were taken?