Chapter 11.1, Problem 44E

To determine

To find: the equation of the parabola.

Answer to Problem 44E

The equation of parabola is $x^2=-12y$ .

Explanation of Solution

The equation of parabola is $x^2=-12y$ .

Given information:

From the figure provided in the question it can be observed that ,

Focus of the parabola is $\left(0,-3\right)$ .

The graph opens downwards.

Calculation:from the given focus it can be observed that the parabola has vertical axis.

So the equation of parabola should be in the following form,

  $x^2-4py$

For parabola with vertical axis, focus is $F\left(0,p\right)$ ,

To comparing the focus it can be observed that,

  $p=-3$

So the equation of parabola is,

  $\begin{array}{l}{x}^2-4py\\ x^2-4\left(-3\right)y\text{ [substitute p by -3]}\\ x^2+12y\text{ [multiply]}\\ x^2=-12y\text{ [simplify]}\end{array}$

Hence, the equation of parabola is $x^2=-12y$ .