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
• Correct answer
  D

  8

Solution

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. $\begin{array}{cc} \Rightarrow & y^2=l x \\ \Rightarrow & (c)^2=\frac{l c^2}{8} \Rightarrow l=8 \end{array}$ $\therefore$ Length of latusrectum $(l)=8$

Hence, the correct answer is option: 'D'.