Find the equation of the chord of the parabol | vedclass

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

Question

(B) The equation of the parabola is $y^2 = 6x$. Comparing this with $y^2 = 4ax$,we get $4a = 6$,so $a = 3/2$.The vertex of the parabola is $(0, 0)$.Th

Vedclass · Accepted Answer

$y + 2x = 0$

Vedclass · Answer

(B) The equation of the parabola is $y^2 = 6x$. Comparing this with $y^2 = 4ax$,we get $4a = 6$,so $a = 3/2$.The vertex of the parabola is $(0, 0)$.The coordinates of the ends of the latus rectum are $(a, 2a)$ and $(a, -2a)$.The negative end of the latus rectum is $(a, -2a) = (3/2, -2 	imes 3/2) = (3/2, -3)$.The chord passes through the vertex $(0, 0)$ and the point $(3/2, -3)$.The slope $m$ of the line passing through $(0, 0)$ and $(3/2, -3)$ is $m = \frac{-3 - 0}{3/2 - 0} = \frac{-3}{3/2} = -2$.The equation of the line is $y - 0 = -2(x - 0)$,which simplifies to $y = -2x$ or $y + 2x = 0$.

Find the equation of the chord of the parabola $y^2 = 6x$ passing through the vertex and the negative end of the latus rectum.

Similar Questions

The equation of a tangent to the parabola $y^2 = 4ax$ making an angle $\theta$ with the $x$-axis is

If two distinct chords drawn from the point $A(4,4)$ on the parabola $y^2=4x$ are bisected by the line $y=ax$,then the interval in which $a$ lies is

What is the length of the latus rectum of the parabola $x^2 = -y$?

$P$ and $Q$ are two points on the parabola $y^2 = 8x$ and $S$ is its focus. $PS$ and $QS$ meet the curve again in $T$ and $R$ respectively. If $PQ$ passes through a fixed point $(-2, 3)$,then $TR$ also passes through a fixed point whose coordinates are

The pole of the line $lx + my + n = 0$ with respect to the parabola $y^{2} = 4ax$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module