Question

Given a parabola with an equation y^2=6x, find the directrix and determine if the parabola opens left or right

Answer 1

The parabola is y² = 6x

This defines a parabola with its vertex at the origin (0,0).
When the equation is compared with y² = 4ax, then
4a = 6
a = 3/2

Therefore the focus is at
(a, 0) = (3/2, 0)
The directrix is located at
(-a, 0) = (-3/2, 0)
The parabola opens right because a > 0.

Answer:
The directrix is x = - 3/2.
The parabola opens right.