New Zealand
Level 8 - NCEA Level 3

# Write Equations of Parabolas

## Interactive practice questions

A parabola has its vertex at the origin. Its focus lies on the $y$y-axis, $4$4 units above the vertex.

State the equation of the parabola.

Easy
Approx 2 minutes

A parabola has its vertex at the origin. It has a focal length measuring $a=4$a=4 units, and its focus lies on the $x$x-axis.

State both possible equations of the parabola.

Find the equation of the parabola with a focus at $\left(0,3\right)$(0,3) and a vertex at the origin. Let $a$a represent the focal length if necessary.

Find the equation of the parabola with a focus at $\left(-6,0\right)$(6,0) and a vertex at the origin. Let $a$a represent the focal length if necessary.

### Outcomes

#### M8-1

Apply the geometry of conic sections

#### 91573

Apply the geometry of conic sections in solving problems