Explanation

(b)
Given,
Focus $S = (0,0)$ let $P(x,y)$ be any point on the parabola,
Since, $SP^{2} = PM^{2}$
$\Rightarrow$ $(x - 0)^{2} + (y - 0)^{2} = (x + a)^{2}$
$\Rightarrow$ $y^{2} = 2ax + a^{2}$ …(i)
$\Rightarrow$ $2y\ \frac{dy}{dx} = 2a$ …(ii)
From Eqs. (i) and (ii), we get
$y^{2} = 2y\ \frac{dy}{dx}.x + \left( y\ \frac{dy}{dx} \right)^{2}$
$\Rightarrow$ $y^{2}\left( \frac{dy}{dx} \right)^{2} + 2xy\ \frac{dy}{dx} = y^{2}$
$\Rightarrow$ $- y\left( \frac{dy}{dx} \right)^{2} = 2x\ \ \frac{dy}{dx} - y$