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

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- 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 : $x=-2$

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