The coordinates of the extremities of the lat | vedclass

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

Question

(B) The given equation of the parabola is $5y^2 = 4x$,which can be rewritten as $y^2 = \frac{4}{5}x$.Comparing this with the standard form $y^2 = 4ax$

Vedclass · Accepted Answer

$(1/5, 2/5), (1/5, -2/5)$

Vedclass · Answer

(B) The given equation of the parabola is $5y^2 = 4x$,which can be rewritten as $y^2 = \frac{4}{5}x$.Comparing this with the standard form $y^2 = 4ax$,we get $4a = \frac{4}{5}$,so $a = \frac{1}{5}$.The focus of the parabola is $(a, 0) = (\frac{1}{5}, 0)$.The latus rectum is a line perpendicular to the axis of the parabola passing through the focus,so its equation is $x = a = \frac{1}{5}$.Substituting $x = \frac{1}{5}$ into the parabola equation $y^2 = \frac{4}{5}x$,we get $y^2 = \frac{4}{5} 	imes \frac{1}{5} = \frac{4}{25}$.Thus,$y = \pm \frac{2}{5}$.Therefore,the coordinates of the extremities of the latus rectum are $(\frac{1}{5}, \frac{2}{5})$ and $(\frac{1}{5}, -\frac{2}{5})$.

The coordinates of the extremities of the latus rectum of the parabola $5y^2 = 4x$ are

Similar Questions

Find the length of the subnormal of the parabola $y^2 = 16x$ at the point where the $x$-coordinate is $4$.

The radius of the smallest circle which touches the parabolas $y = x^2 + 2$ and $x = y^2 + 2$ is

The locus of the mid-points of all chords of the parabola $y^{2}=4ax$ passing through its vertex is another parabola with directrix:

The line $x \cos \alpha + y \sin \alpha = p$ will touch the parabola $y^2 = 4a(x + a)$ if:

$A$ tangent is drawn to the parabola $y^{2}=6x$ which is perpendicular to the line $2x+y=1$. Which of the following points does $NOT$ lie on it?

Vedclass Test Series

Exam Paper Generator

Online Exam Module