Chapter 9.3, Problem 6ST

To determine

To find: The equation of the parabola.

Answer to Problem 6ST

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

Explanation of Solution

Given information: It is given, $V\left(-4,3\right)$ and $F\left(0,3\right)$ .

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

  $\therefore x^2=4ay$

Coordinate of focus $\left(0,a\right)$ .

  $\begin{array}{l}\left(0,a\right)=\left(0,3\right)\\ a=3\end{array}$

Therefore, required equation is

  $\begin{array}{l}{x}^2=4\times 3\times y\\ x^2=12y\end{array}$