create the differention equation from x^2 +y^2 +2ax+2by+c=0


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Question Number 115830 by mohammad17 last updated on 28/Sep/20

$c r e a t e t h e d i f f e r e n t i o n e q u a t i o n f r o m$ $x^{2} + y^{2} + 2 a x + 2 b y + c = 0$
Commented by bemath last updated on 29/Sep/20

$\Rightarrow x^{2} + 2 a x + a^{2} + y^{2} + 2 b y = a^{2} + b^{2} - c$ $\Rightarrow {(x + a)}^{2} + {(y + b)}^{2} = a^{2} + b^{2} - c$ $\Rightarrow \frac{d}{d x} [{(x + a)}^{2} + {(y + b)}^{2}] = 0$ $2 (x + a) + 2 (y + b) y^{'} = 0$ $\Rightarrow y^{'} = - \frac{(x + a)}{(y + b)}$
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