# Find the coordinates of the focus, axis of the parabola,

Question:

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

Solution:

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

Here, the coefficient of $x$ is positive. Hence, the parabola opens towards the right.

On comparing this equation with $y^{2}=4 a x$, we obtain

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

$\therefore$ Coordinates of the focus $=(a, 0)=\left(\frac{5}{2}, 0\right)$

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

Equation of directrix, $x=-a$, i.e., $x=-\frac{5}{2}$

Length of latus rectum = 4a = 10