Chapter 9.3, Problem 10WE

To determine

To graph: Find the equation and plot the graph accordingly.

Explanation of Solution

Given information: It is given that $F\left(3,0\right)andV\left(0,0\right)$ .

Calculation: Since, focus lies on y-axis.

Hence, the equation will be either $y^2=4ax\&y^2=-4ax$

But, focus has a negative y-coordinate, hence, we use equation $y^2=4ax$

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

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

Hence,

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

Therefore, the required equation of parabola is $y^2=12x$

Graph: The required graph is given below.

  

Interpretation: Parabola $y^2=12x$ has the vertex of $\left(0,0\right)$ . And its focus is $\left(3,0\right)$ .