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  4. The equation of the curve whose subnormal is constant ' a ' is

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Q. The equation of the curve whose subnormal is constant ' $a$ ' is

Differential Equations

Solution:

$L_{s N }=y \frac{d y}{d x}$
$y \frac{d y}{d x}=a$
$\Rightarrow \frac{y^2}{2}=a x+C_2 $
$ \Rightarrow y^2=2 a x+b$