Let P Q be a chord of the parabola y^2=12 x and the midpoint of P Q be at (4,1).

Question

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

Accepted Answer

${y}^{2}=12x$

Chord $PQ$ having mid-point $({x}_{1},{y}_{1})=(4,1)$ equation of chord $PQ$

$\begin{gathered} T={S}_{1} \ y{y}_{1}-12\frac{(x+{x}_{1})}{2}={y}_{2}^{1}-12{x}_{1} \ y-6(x+4)=1-12	imes 4 \ y-6x-24=-47 \ y-6x+23=0 \end{gathered}$

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

$-20-6	imes \frac{1}{2}+23=0$

Solutions · 1