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# del operator? watch

1. two circles have eqns x^2 + y^2 + 2ax + 2by + c = 0 and x^2 + y^2 + 2a'x + 2b'y + c' = 0. show they are orthogonal if 2aa' + 2bb' = c+c'

ok so just looked up what orthogonal circles look like..

just not sure how to approach the problem - any hints?

do you find the two points of intersection the find the tangents at those points or something?

thanks
2. bump!
3. They're orthogonal if their tangents at the points of intersection are orthogonal, so you need to
(i) Find the points of intersection (say P and Q)
(ii) Find the gradient of both circles at P and Q, and find the conditions required for them to be orthogonal

I don't think you need to use a del operator here.
4. hey. thanks.

sorry I may be being stupid, but i can't see how to find the points of intersection

i see we have two equations, 2 unknowns x,y but how do i solve?
5. Subtract one equation from the other to get a linear equation in x and y. Use this to write y as a function of x and then sub back into one of the original circles.

Although to be honest I think you'd be better off drawing a sketch and doing a little geometry.
6. thanks okay. So why is this in the partial derivatives chapter?
7. ahh you are right..algebraic method is unwieldy! Tips on geometric one?

so i know there are two circles, and i know their radii and centres..
8. ??

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