Explanation

(d)
Let family of circles be
$(x - \alpha)^{2} + (y - 2)^{2} = 5^{2}$
$\Rightarrow$ $x^{2} + \alpha^{2} - 2\alpha x + y^{2} - 21 - 4y = 0$ …(i)
$\Rightarrow$ $2x - 2\alpha + 2y\ \frac{dy}{dx} - 4\frac{dy}{dx} = 0$
$\Rightarrow$ $\alpha = x + \frac{dy}{dx}(y - 2)$
On putting the value of $\alpha$ in Eq. (i), we get
$\left( x - x - \frac{dy}{dx}(y - 2) \right)^{2} + (y - 2)^{2} = 5^{2}$
$\Rightarrow$ $\left( \frac{dy}{dx} \right)^{2}(y - 2)^{2} = 25 - (y - 2)^{2}$