Question

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.

Focus at $\left(4,0\right)$and vertex at$\left(0,0\right)$.

Short answer

The equation will be $y^2=16x$.

The graph of an equation will be :

Step-by-step solution

Step 1. Given Information.

The focus is at$\left(4,0\right)$and its vertex is at$\left(0,0\right)$.

Step 2.  Observations.

Observe the vertex and focus points, the y-coordinates are same and on x-axis.

Thus, the parabola is horizontal.

Step 3. Calculation of an equation and graphing.

The distance from the vertex $\left(0,0\right)$to the focus $\left(4,0\right)$is $a=4$.

So, the equation of the parabola is $y^2=4ax$.

As $a=4\Rightarrow y^2=16x$.

The two points that joining the two points is$\left(a,2a\right)$and$\left(a,-2a\right)$.

Step 4. The latus rectum.

As $x=4$,

$$\begin{gathered} y^2=16x=16\left(4\right) \\ {y}^2=64 \\ y=\pm 8 \end{gathered}$$

The points will be $\left(4,8\right)$and $\left(4,-8\right)$determine the latus rectum.

The graph will be :