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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

$8$

Vedclass · Answer

(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

Similar Questions

If $m_1$ and $m_2$ are the slopes of the tangents drawn from the point $(2, 3)$ to the parabola $y^2 = 4x$,then what is the value of $\frac{1}{m_1} + \frac{1}{m_2}$?

What are the coordinates of the endpoints of the latus rectum of the parabola $(y - 1)^2 = 4(x + 1)$?

If $P(-3, 2)$ is an end point of the focal chord $PQ$ of the parabola $y^2 + 4x + 4y = 0$,then the slope of the normal drawn at $Q$ is

If $(x_1, y_1)$ and $(x_2, y_2)$ are the end points of a focal chord of the parabola $y^2 = 5x$,then $4x_1x_2 + y_1y_2$ is equal to

The length of the chord of the parabola $x^2 = 4y$ having the equation $x - \sqrt{2}y + 4\sqrt{2} = 0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module