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

5. 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

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Given, a parabola with equation 

y^2 =10x

This is parabola of the form y^2=4ax which opens towards the right.

So,

By comparing the given parabola equation with the standard equation, we get,

4a=10

a=\frac{10}{4}=\frac{5}{2}

Hence,

Coordinates of the focus :

(a,0)=\left(\frac{5}{2},0\right)

Axis of the parabola:

It can be seen that the axis of this parabola is X-Axis.

The equation of the directrix

x=-a,\Rightarrow x=-\frac{5}{2}\Rightarrow x+\frac{5}{2}=0\Rightarrow 2x+5=0

The length of the latus rectum:

4a=4(\frac{5}{2})=10.

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