# Find the axies, vertex, focus, equation of directrix , latus rectum , length of the latus rectum for the following parabolas and hence sketch their graphs. $y^{2}=-8x$

This is the first part of the multi-part question Q2

Toolbox:
• Standard parabolas :
• (i)$y^2=4ax$
• In this case the axis of symmetry is $x$-axis.
• The focus is $F(a,0)$ and the equation of the directrix is $x=-a$
• (ii)$y^2=-4ax$
• In this case the focus is $F(-a,0)$ and the equation of directrix is $x=a$
• (iii)$x^2=4ay$
• In this case the axis of symmetry is $y$-axis.
• The focus is $F(0,a)$ and the equation of directrix is $y=-a$
• (iv)$x^2=-4ay$
• In this case the focus is $F(0,-a)$ and the equation of directrix is $y=a$
Step 1:
$y^2=-8x$
This is of the form $y^2=-4ax$
Where $4a=8$
$\Rightarrow a=2$
The parabola opens leftwards.
Step 2:
Axis : $y=0$
Vertex : (0,0)
Focus : $(-2,0)$
Equation of directrix : $x=2$
Length of latus rectum=8.
Equation of latus rectum : $x=-2$
edited Jun 16, 2013