Answer: $A$
Equation of the chord passing the focal point of the parabola $\mathrm{y^2 = 4ax}$ is $\mathrm{y = m(x-a)}$
$\textrm x-$coordinates of the intersection of this line to the parabola are the solutions of equation.
$\Rightarrow \mathrm {m^2(x-a)^2 = 4ax}$
$\Rightarrow \mathrm {m^2.x^2-2a(m^2+2)x+m^2.a^2 = 0}$
Product $\mathrm {x_1.x_2 = \frac{m^2.a^2}{m^2} = a^2}$
${\therefore \mathbf A}$ is the correct answer.