If the straight line y=mx+c is parallel to th | vedclass

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(D) The axis of the parabola $y^2=lx$ is the $x$-axis,which has the equation $y=0$.Since the line $y=mx+c$ is parallel to the $x$-axis,its slope $m$ m

Vedclass · Accepted Answer

$8$

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(D) The axis of the parabola $y^2=lx$ is the $x$-axis,which has the equation $y=0$.Since the line $y=mx+c$ is parallel to the $x$-axis,its slope $m$ must be $0$.Thus,the equation of the line becomes $y=c$.Given that the line intersects the parabola at the point $\left(\frac{c^2}{8}, cight)$,this point must satisfy the equation of the parabola $y^2=lx$.Substituting $y=c$ and $x=\frac{c^2}{8}$ into the equation $y^2=lx$:$c^2 = l \left(\frac{c^2}{8}ight)$Assuming $c 
eq 0$,we can divide both sides by $c^2$:$1 = \frac{l}{8}$$l = 8$The length of the latus rectum of the parabola $y^2=lx$ is $l$.Therefore,the length of the latus rectum is $8$.

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 latus rectum is

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