Find the coordinates of the focus, axis of the parabola, the equation of directrix

Question:

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for $y^{2}=12 x$

Solution:

The given equation is $y^{2}=12 x$.

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

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

$4 a=12 \Rightarrow a=3$

$\therefore$ Coordinates of the focus $=(a, 0)=(3,0)$

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

Equation of direcctrix, $x=-a$ i.e., $x=-3$ i.e., $x+3=0$

Length of latus rectum $=4 a=4 \times 3=12$

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