Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum. y^2 = 10x

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 = 10x

Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum. y^2 = 10x

Given:

The condition is

${{y}^{2}}~=\text{ }10x$

.

Here we realize that the coefficient of

$x\text{ }is\text{ }positive$

.

Along these lines, the parabola opens towards right .

On contrasting this condition and

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

, we get,

$\begin{array}{*{35}{l}} 4a\text{ }=\text{ }10 \\ a\text{ }=~10/4\text{ }=\text{ }5/2 \\ \end{array}$

Accordingly, the co-ordinates of the concentration

$=\text{ }\left( a,0 \right)\text{ }=\text{ }\left( 5/2,\text{ }0 \right)$

Since, the given condition includes

${{y}^{2}}$

, the axis of the parabola is the

$x-axis$

.

∴ The condition of directrix,

$x\text{ }=-a$

, then, at that point,

$x\text{ }=\text{ }\text{ }5/2$

Length of latus rectum

$=\text{ }4a\text{ }=\text{ }4\left( 5/2 \right)\text{ }=\text{ }10$

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