Mathematics - Parabola Question with Solution | TestHub

$y-\sqrt{3}x+3=0$ can be rewritten as

$\frac{y-0}{\frac{\sqrt{3}}{2}}=\frac{x-\sqrt{3}}{\frac{1}{2}}=r$

Solving $(A)$ with the parabola

$y^2=x+2\frac{3r^2}{4}-\frac{r}{2}-\sqrt{3}-2=0\Rightarrow PA\cdot PB=r_1{r}_2=\frac{4(\sqrt{3}+2)}{3}$