Find the coordinates of the focus axis of the parabola the equation of directrix and the length of the latus rectum for $y^{2}$ $= - 8 x$

Question

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Answer 1

The given equation is $y^{2} = - 8 x$
Here the coefficient of $x$ is negative.
Hence the parabola opens towards the left.
On comparing this equation with $y^{2} = - 4 a x$
$- 4 a = - 8$
$\Rightarrow a = 2$
$∴$ Coordinates of the focus $= (- a, 0) = (- 2, 0)$
Axis of the parabola is the $x$ -axis i.e. $y = 0$
Equation of directrix $x = a$ i.e., $x = 2$
Length of latus rectum $= 4 a = 8$

Answer 2

The given equation is

y^{2} = - 8 x

Here the coefficient of

x

is negative.
Hence the parabola opens towards the left.
On comparing this equation with

y^{2} = - 4 a x

- 4 a = - 8

\Rightarrow a = 2

∴

Coordinates of the focus

= (- a, 0) = (- 2, 0)

Axis of the parabola is the

x

-axis i.e.

y = 0

Equation of directrix

x = a

i.e.,

x = 2

Length of latus rectum

= 4 a = 8