Verified Solution • 2025–26 Session moderate

QJEEM24Mab6e4: JEE Main 2024 Mathematics - Class 11 JEEM24Mab6e4 Solution: Let be a chord of the parabola and the midpoint of be at .…

Let PQP Q be a chord of the parabola y2=12xy^2=12 x and the midpoint of PQP Q be at (4,1)(4,1) . Then, which of the following point lies on the line passing through the points P\mathrm{P} and Q\mathrm{Q} ?

Multiple Choice Options

  • A (3,−3)(3,-3)
  • B (12,−20)\left(\frac{1}{2},-20\right)
  • C (2,−9)(2,-9)
  • D (32,−16)\left(\frac{3}{2},-16\right)

Step-by-Step Verified Solution

y2=12xy^2=12 x

Chord PQP Q having mid-point (x1,y1)=(4,1)(x_1, y_1)=(4,1) equation of chord PQP Q

amp;T=S1amp;yy1−12(x+x1)2=y12−12x1amp;y−6(x+4)=1−12×4amp;y−6x−24=−47amp;y−6x+23=0\begin{aligned}& T=S_1 \\& y y_1-12 \frac{\left(x+x_1\right)}{2}=y_1^2-12 x_1 \\& y-6(x+4)=1-12 \times 4 \\& y-6 x-24=-47 \\& y-6 x+23=0\end{aligned}

From option (4) x=12x=\frac{1}{2} & y=−20y=-20

−20−6×12+23=0-20-6 \times \frac{1}{2}+23=0

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