Chapter 9.3, Problem 13WE

To determine

To find: The equation of the parabola.

Answer to Problem 13WE

The required equation of the parabola is $x^2=8y$ .

Explanation of Solution

Given information: It is given, $F\left(0,2\right)andx=2$ .

Formula used: $x^2=4ayor{x}^2=-4ay$

Calculation: Since focus lies on y-axis.

Therefore, equation is either $x^2=4ayor{x}^2=-4ay$

Since focus has positive y-coordinate

  $\therefore x^2=4ay$

The coordinates of focus $\left(0,a\right)$ ,

  $\begin{array}{l}\left(0,a\right)=\left(0,2\right)\\ a=2\end{array}$

Therefore, required equation is

  $\begin{array}{l}{x}^2=4\times 2\times y\\ x^2=8y\end{array}$

Now, graph the parabola,