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…

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?
  1. $(3,-3)$
  2. $(2,-9)$
  3. $\left(\frac{3}{2},-16\right)$
  4. $\left(\frac{1}{2},-20\right)$

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

Asked in: JEE Main 2024 (04 Apr Shift 2)

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