Find the differential equation by eliminating arbitrary constants… - Vidyadip

Question

Find the differential equation by eliminating arbitrary constants from the relation $x^2 + y^2 = 2ax$

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Answer

$x^2+y^2=2 a x\ldots(i)$
Here, a is an arbitrary constant.
Differentiating (i) w.r.t. $x$, we get
$ 2 x+2 y \frac{ d y}{ d x}=2 a$
$\therefore 2 x+2 y \frac{ d y}{ d x}=\frac{x^2+y^2}{x} \ldots . . .[\text { From (i)] }$
$\therefore 2 x^2+2 x y \frac{ d y}{ d x}= x ^2+ y ^2$
$\therefore 2 x y \frac{ d y}{ d x}= y ^2- x ^2 $

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