Explanation

(b)
Equation of chord of hyperbola $x^{2} - y^{2} = a^{2}$ with mid point as $(h,\ k)$ is give by
$xh - yk = h^{2} - k^{2}$
$\Rightarrow y = \frac{h}{k} \times \frac{(h^{2} - k^{2})}{k}$
This will touch the parabola $y^{2} = 4ax,$ if
$- \left( \frac{h^{2} - k^{2}}{k} \right) = \frac{a}{h/k}$
$\Rightarrow \ ak^{2} = - h^{3} + k^{2}h$
$\therefore\$Locus of the mid point is $x^{3} = y^{2}(x - a)$