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

Given relation is
$x^2+y^2=2 a x\ldots(i)$
Differentiating w.r.t. $x$, we get
$2 x+2 y \frac{ d y}{ d x}=2 a\ldots(ii)$
Substituting (ii) in (i), we get
$ x ^2+ y ^2=\left(2 x+2 y \frac{ d y}{ d x}\right) x$
$\therefore x ^2+ y ^2=2 x^2+2 x y \frac{ d y}{ d x} $
$\therefore 2 x y \frac{ d y}{ d x}= y ^2- x ^2$, which is the required differential equation.

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