Question

The equation of line(s) joining the vertex of $y^2=6x$ to the point on it whose abscissa is $24,$ is (are)

• A. $2y+x+1=0$
• B. $2y-x+1=0$
• C. $x+2y=0$
• D. $x-2y=0$

Answer 1

Answer: (C), (D)

The correct options are
C $x+2y=0$
D $x-2y=0$

Given, $y^2=6x$
Vertex is $(0,0)$
For $x=24,$
$y^2=24\times 6=144$
$\Rightarrow y=\pm 12$
$\therefore$ Two points are possible on the parabola, $(24,12)$ and $(24,-12)$

Equation of line joining the point $(0,0)$ and $(24,12)$ is
$y-0=\frac{12-0}{24-0}(x-0)$
$\Rightarrow y=\frac{1}{2}x$
$\Rightarrow 2y-x=0$

Similarly, equation of line joining the point $(0,0)$ and $(24,-12)$ is
$y-0=\frac{-12-0}{24-0}(x-0)$
$\Rightarrow y=-\frac{1}{2}x$
$\Rightarrow 2y+x=0$