Question

Find the equation of curve whose subnormal constant

Answer 1

we know length of subnormal = $y\frac{dy}{dx}$

According to question,
$y\frac{dy}{dx}=C$, where C is constant

$\int{y}\,dy=C\int\,dx$

$\frac{y^2}{2}=Cx+D$, D is constant

$y^2=2Cx+2D$

we can write it $y^2=Px+Q$
where P and Q are constant