Let PQ be a chord of the parabola $y^2=12 x$ and the midpoint of PQ be at $(4,1)$. Then, which of the following point lies on the line passing through the points $\mathrm{P}$ and Q?

• A

  $(3,-3)$
• B

  $(2,-9)$
• C

  $\left(\frac{3}{2},-16\right)$
• Correct answer
  D

  $\left(\frac{1}{2},-20\right)$

Solution

$\begin{aligned} & T=S_1 \\ & y-6(x+4) \\ & =1-48 \\ & 6 x-y=23 \end{aligned}$
Option $4\left(\frac{1}{2},-20\right)$ will satisfy

Hence, the correct answer is option: 'D'.