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 $x^{2}=6 y$

Solution:

The given equation is $x^{2}=6 y$.

Here, the coefficient of is positive. Hence, the parabola opens upwards.

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

$4 a=6 \Rightarrow a=\frac{3}{2}$

$\therefore$ Coordinates of the focus $=(0, a)=\left(0, \frac{3}{2}\right)$

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

Equation of directrix, $y=-a$ i.e., $y=-\frac{3}{2}$

Length of latus rectum $=4 a=6$

Administrator

Leave a comment

Please enter comment.
Please enter your name.