Explanation

(d)
The centre and radius of given circle are $(r,\ h)$ and $r$
Thus, $x = 0$ is one of tangent
Let another tangent is $y = mx$ to the circ le. This line will be tangent, if
$\frac{h - mr}{\sqrt{1 + m^{2}}} = r$
$\Rightarrow \ \ \ m = \left( \frac{h^{2} - r^{2}}{2hr} \right)$
Therefore, equation of tangent is
$y = \frac{(h^{2} - r^{2})}{2hr}x$
$\Rightarrow \ \ \left( h^{2} - r^{2} \right)x - 2hr\ y = 0$
Required tangents are $x = 0$ and $\left( h^{2} - r^{2} \right)x - 2hry = 0$