Question

Find the coordinates of the focus, the axis of the parabola, the equation of directrix, and the length of the latus rectum 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 $x^2= 4ay$, we obtain

$4a = 6$ $x^2$$$

$a = 6/4$

$= 3/2$

∴Coordinates of the focus = $(0, a)$ $=(0, 3/2)$
Since the given equation involves $x^2$, the axis of the parabola is the y-axis.
Equation of directrix, $y =-a$ i.e, $y = -3/2$
Length of the latus rectum $=$ $4a= 6.$