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Let $\mathrm{PQ}$ be a focal chord of the parabola $\mathrm{ y^{2} = 36x}$ of length 100, making an acute angle with the positive x-axis. Let the ordinate of $\mathrm{ P}$ be positive and M be the point on the line segment $\mathrm{ PQ}$ such that $\mathrm{ PM:MQ = 3:1}$ . Then which of the following points does NOT lie on the line passing through $\mathrm{ M}$ and perpendicular to the line $\mathrm{ PQ}$ ?
Option: 1
$\left ( 3,33 \right )$

Option: 2
$\left ( 6,29 \right )$

Option: 3
$\left ( -6,45 \right )$

Option: 4
$\left ( -3,43 \right )$

Answers (1)

best_answer

$\mathrm{\begin{aligned} & 9\left(t+\frac{1}{t}\right)^2=100 \\ \end{aligned}}$

$\mathrm{ t=3 }$

$\begin{aligned} & \Rightarrow \mathrm{P}(81,54) \& Q(1,-6) \\ \end{aligned}$

$\mathrm{M(21,9) }$

$\begin{aligned} & \Rightarrow \mathrm{L} \text { is }(\mathrm{y}-9)=\frac{-4}{3}(x-21) \\ \end{aligned}$

$\begin{aligned} & 3 \mathrm{y}-27=-4 x+84 \\ & 4 \mathrm{x}+3 \mathrm{y}=111 \end{aligned}$

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