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

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

Vedclass · Accepted Answer

$8$

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(D) The equation of the parabola is $y^2=lx$. The axis of this parabola is the $x$-axis,which has the equation $y=0$. Since the line $y=mx+c$ is parallel to the axis of the parabola $(y=0)$,its slope $m$ must be $0$. Thus,the line is $y=c$. Given that the point $\left(\frac{c^2}{8}, cight)$ lies on the parabola $y^2=lx$,it must satisfy the equation: $c^2 = l \left(\frac{c^2}{8}ight)$ $c^2 = \frac{lc^2}{8}$ Assuming $c 
eq 0$,we can divide both sides by $c^2$: $1 = \frac{l}{8} \Rightarrow l = 8$. 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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