Explanation

(b)
$y = mx + c$ is tangent to $x^{2} + y^{2} = a^{2}$, if
$c = \pm \sqrt{1 + m^{2}}$
Since, $y = - \frac{lx}{m} + \frac{1}{m}$ is tangent to $x^{2} + y^{2} = a^{2}$, if
$\frac{1}{m} = \pm \frac{a}{m}\sqrt{l^{2} + m^{2}}\left\lbrack \because\ \ c = a\sqrt{\left( 1 + m^{2} \right)} \right\rbrack$
$\Rightarrow \ \ \ \ l^{2} = m^{2} = \frac{1}{a^{2}}$
Hence, locus of point $(l,\ m)$ is $x^{2} + y^{2} = \frac{1}{a^{2}}$