Question

Find the equations of the lines joining the vertex of the parabola $y^2=6x$ to the point on it which have abscissa 24.

Answer 1

Let P and Q be points on the parabola $y^2=6x$ and OP,OQ be the lines joining the vertex O to the points P and Q whose abscissa are 24.

Thus

$y^2=6\times 24=144ory=\pm 12$

Therefore the coordinates of the points P and Q are (24,12) and B(24,-12) respectively.

Hence the lines are

$y=\pm \frac{12}{24}x\Rightarrow 2y=\pm x$