Question

If the straight line $y=mx+c$ is parallel to the axis of the parabola $y^2=lx$ 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, $y^2=lx\dots (i)$
Here, length of latusrectum $=l$
Since, point $\left(\frac{c^2}{8},c\right)$ is the point of intersection of parabola and the line $y=mx+c$ then it will satisfy the equations.
$\Rightarrow y^2=lx$
$\Rightarrow (c{)}^2=\frac{l{c}^2}{8}$
$\Rightarrow l=8$
$\therefore$ Length of latusrectum $(l)=8$