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Originally posted by newton

I am trying to simplify the following equation:

((x+c)+y) + ((x-c)+y) = 2a

to get: x/a + y/(a - c) = 1.
I brought the second radical to the right side of the equation, squared and start simplifying:

(x+c)+y = 4a-4a ((x-c)+y) + (x-c)+y
(x+c)+y) - (x-c)-y = 4a - 4a((x-c)+y)
(x+c) - (x-c) = 4a-4a((x-c)+y)
4cx = 4a-4a((x-c)+y)
cx = a-a((x-c)+y)
cx - a = -a((x-c)+y)<---Square both sides again and simplify

However I get equation of hyperbola from there - check your signs
How do I proceed from here, to get what I want above?

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