Question

Find the coordinates of the focus, axis of the parabola ,the equation of directrix and the length of the latus reactum for $x$ ${}^2=6y$

Answer 1

The given equation is $x^2=6y$
Here the coefficient of $y$ is positive.
Hence the parabola opens upwards
On comparing this equation with $x^2=4ay$,
$4a=6$
$\Rightarrow a=\frac{3}{2}$
$\therefore$ Coordinates of the focus $=(0,a)=(0,\frac{3}{2})$
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 $=4a=6$