Chapter 12.7, Problem 9MRE

To determine

To determine the equation of each figure described.

Answer to Problem 9MRE

  $y=-\frac{x^2}{8}$

Explanation of Solution

Given information :

The parabola with focus (0, -2) and directrix y=-2

Equation of parabola is,

  ${\left(x-h\right)}^2=4p\left(y-k\right)$

Where focus is $\left(h,k+p\right)$ and directrix is $y=k-p$

Hence the required equation is,

  $\begin{array}{l}{\left(x-0\right)}^2=4\left(-2\right)\left(y-0\right)\\ x^2=-8y\\ y=-\frac{x^2}{8}\end{array}$