Answer
$$ \quad 2|p|=\rho$$
Work Step by Step
We find:
$\frac{\left|x^{\prime} y^{\prime \prime}-y^{\prime} x^{\prime \prime}\right|}{\left(x^{\prime 2}+y^{\prime 2}\right)^{3 / 2}}= \kappa$
Let $t=y=t,$ and then
$\frac{t^{2}}{4 p}=x$
$C A S:$
$\frac{1 /|2 p|}{\left[t^{2} /\left(4 p^{2}\right)+1\right]^{3 / 2}}=\kappa(t)$
$t=0$ when $(x, y)=(0,0)$ so
$$ \quad 2|p|=\rho$$
