Question

The equation of the lines joining the vertex of the parabola $y^2$=6x to the points on it whose abscissa is 24, is

• A. $y\pm 2x=0$
• B. $2y\pm x=0$
• C. $x\pm 2y=0$
• D. $2x\pm 2y=0$

Answer 1

The correct option is B $2y\pm x=0$

Let $A$ and $B$ be points on the parabola $y^2=6x$ and $OA,$ $OB$ be the lines joining the vertex $O$ to the points $A$ and $B$ whose abscissa are $24$

Now,

$y^2=6\times 24$

$\Rightarrow$ $y^2=144$

$\Rightarrow$ $y=\pm 12$

$\therefore$ The co-ordinates of the points $A$ and $B$ are $(24,12)$ and $(24,-12)$ respectively.

$\Rightarrow$ $y-0=\frac{\pm 12-0}{24-0}(x-0)$

$\Rightarrow$ $y=\pm \frac{1}{2}x$

$\Rightarrow$ $2y=\pm x$

$\therefore$ $2y\pm x=0$