Question

For the given parabola find the coordinates of focus, axis, the equation of the directrix and the length of the latus rectum.
$y^2=8x$

Answer 1

Given equation is $y^2=8x$

Since the above equation is involves $y^2$

Its axis is x-axis

Also coefficient of $x$ is positive

Hence we use equation

$y^2=4ax$

Comparing

$y^2=8x$.......(1)

$y^2=4ax$........(2)

From (1) and (2)

$4ax=8x$

$a=\frac{8x}{4x}$

$a=2$

Coordinates of focus is (a,0)

$=(2,0)$

Equation of Directrix is

$x=-a$

$x=-2$

Lactus Rectum is $4a$

$=4\times 2$

$=8$