Question

If the straight line $y=m x+c$ is parallel to the axis of the parabola $y^{2}=l x$ and intersects the parabola at $\left(\frac{c^{2}}{8}, c\right)$, then the length of the latusrectum is

• A. 2
• B. 3
• C. 4
• D. 8

Answer 1

Answer: (D)

Given equation of parabola, $y^{2}=l x \,\,\,\ldots( i )$
Here, length of latusrectum $=l$
Since, point $\left(\frac{c^{2}}{8}, c\right)$ is the point of intersection of parabola and the line $y=m x+c$ then it will satisfy the equations.
$\Rightarrow y^{2}=l x$
$\Rightarrow (c)^{2}=\frac{l c^{2}}{8}$
$ \Rightarrow l=8$
$\therefore $ Length of latusrectum $(l)=8$