Q. 54.0( 17 Votes )

# In each of the following, 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

Answer :

The given equation is y^{2} = 10x

Here, the coefficient of x is positive.

Hence, the parabola open towards the right.

On comparing this equation with y^{2} = -4ax, we get,

4a = 10

⇒ a =

Thus,

Co-ordinates of the focus = (a,0) =

Since, the given equation involves y^{2}, the axis of the parabola is the x-axis.

Equation of directrix, x =-a, then,

x =

Length of latus rectum = 4a = 10

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