Question

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

Answer 1

The parabola $y^2=6x$ is symmetric about $x-$ axis. So, for a given abscissa there will be two points on the parabola as shown in Fig $25.39$.

Let $P$ and $Q$ be two points on the parabola whose absicssa is

$24$. Let their coordinates be $(24,y_1)$ and $(24,-y_1)$ respectively.

Since $P(24,y_1)$ lies on $y^2=6x$.

$\therefore y_1^2=6\times 24\Rightarrow y_1=12$

So, the coordinates of $P$ and $Q$ are $(24,12)$ and $(24,-12)$ respectivety.

The equation $OP$ and $OQ$ are

$y-0=\frac{12-0}{24-0}(x-0)$ and $y-0=\frac{-12-0}{24-0}(x-0)$
or, $x=2y$ and $x=-2y$ respectively.