Chapter 11.1, Problem 34E

To determine

To find: the equation of the parabola.

Answer to Problem 34E

The equation of parabola is $x^2=-24y$ .

Explanation of Solution

The equation of parabola is $x^2=-24y$ .

Given information:

Vertex $\left(0,0\right)$

Directrix $y=6$

Calculation: from the given directrix it can be observed that the parabola has virtical axis.

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

  $x^2-4py$

For parabola with horizontal axis, directrix is $y=-p$ .

To comparing the directrix it can be observed that,

  $p=-6$

So the equation of parabola is,

  $\begin{array}{l}{x}^2-4py\\ x^2-4\left(-6\right)y\text{ [substitute p by -6]}\\ x^2+24y\text{ [multiply]}\\ x^2+24y=0\text{ [simplify]}\\ x^2=-24y\end{array}$

Hence, the equation of parabola is $x^2=-24y$ .