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

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

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

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

Given:

The condition is

${{y}^{2}}~=\text{ }-8x$

Here we realize that the coefficient of $x$ is negative.

Along these lines, the parabola opens towards left.

On contrasting this condition and

${{y}^{2}}~=\text{ }-4ax$

, we get,

$\begin{array}{*{35}{l}} -4a\text{ }=\text{ }-8 \\ a\text{ }=\text{ }-8/-4\text{ }=\text{ }2 \\ \end{array}$

Accordingly, the co-ordinates of the concentration

$~=\left( -a,0 \right)\text{ }=\text{ }\left( -2,\text{ }0 \right)$

Since, the given condition includes

${{y}^{2}}$

, the hub of the parabola is the

$x$

axis .

∴ The condition of directrix,

$x\text{ }=a$

, then, at that point,

$x\text{ }=\text{ }2$

Length of latus rectum

$=\text{ }4a\text{ }=\text{ }4\text{ }\left( 2 \right)\text{ }=\text{ }8$

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