Question

Identify the focus, directrix, and axis of symmetry of the parabola 6x2+3y=0

Answer 1

Manipulate the equation to get it in one of the following forms: 
$x^{2} = 4py$ or $y^2=4px$

Subtract 3y from both sides of the equation: $6 x^{2} =-3y$ 
Divide by 6 on both sides of the equation (reduce): $x^{2} =- \frac{1}{2}y$
This is a parabola that opens down and the value of p = $- \frac{1}{8}$.
The vertex is at the origin (0, 0)
Focus: (0, 0 + p) ⇒ $(0, - \frac{1}{8} )$
Directrix: y = 0 - p ⇒ $y = \frac{1}{8}$
Axis of Symmetry: x = 0