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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
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The correct answer is:
8
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 $(l)=8$
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