<div class="clay6-step-odd"><div class="clay6-basic" id="pr10">$(a)\;x-6y=26$ is the correct answer since $(2,-4)$ is the midpoint, </div><div class="clay6-basic" id="pr11">it lies on the line of chord.</div><div class="clay6-basic" id="pr12">$\Rightarrow\:$ (2,-4)$ should satisfy the equation of the chord.</div><div class="clay6-basic" id="pr13">But $(2,-4)$ satisfies only equation $x-6y=26$ out of the $4$ options.</div><div class="clay6-basic" id="pr14">$\therefore (a) is the correct answer.</div></div>