Question

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

Answer 1

Step $1$: Comparing with the general form of Parabola
Given $y^2=8x$
The given equation involves $y^2$, so the axis of symmetry is along the $x-$ axis.
The coefficient of $x$ is positive, so the parabola opens to the right.
Comparing $y^2=8x$ (Given) with $y^2=4ax$ (general form), we get $a=2$

Step $2$: Finding Focus
$\therefore$ Coordinates of focus is $=(a,0)$
$=(2,0)$
$a=2$

Step $3$ : Equation of Directrix
Equation of Directrix is
$x=-a$
$\Rightarrow x=-2$
Length of Latus Rectum is $=4a$
$=4\times 2$
$=8\text{units}$.