Chapter 11.3, Problem 8MRE

To determine

To calculate:

The solution of the parabola with the focus $\left(0,-1\right)$ and its directrix is $y-1$

Answer to Problem 8MRE

The equation of the parabola is $x^2=-4y$ .

Explanation of Solution

Given information:

  $\begin{array}{l}h=0\\ k=0\\ p=-1\end{array}$

Calculation:

The directrix is horizontal; the axis of the symmetry is vertical.

The standard equation of the form:

  ${\left(x-h\right)}^2=4p\left(y-k\right)\mathrm{...}\left(1\right)$

Put the value in (1):

  $\begin{array}{l}{\left(x-0\right)}^2=4\left(-1\right)\left(y-0\right)\\ x^2=-4y\end{array}$

The equation of the parabola is $x^2=-4y$ .