Question

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

Vertex at $\left(-1,-2\right)$; focus at$\left(0,-2\right)$

Short answer

The equation of parabola is$x=\frac{y^2}{4}+y$ .The latus rectum is $x=0$.

The graph of the equation shown below

Step-by-step solution

Step 1. Given information .

Consider the given vertex and focus points .

.  Standard form of parabola .

The standard form of parabola is $x=\frac{1}{4\left(f-h\right)}{\left(y-k\right)}^2+h$where $\left(h,k\right)$is vertex and$\left(f,k\right)$is focus .

Step 3. Find the equation of parabola .

To find the equation of parabola substitute the values in standard form.

$$\begin{gathered} x=\frac{1}{4\left(f-h\right)}{\left(y-k\right)}^2+h \\ x=\frac{y^2}{4}+y \end{gathered}$$

The latus rectum is parallel to the directrix and passes through the focus

$x=0$.

Step 4.  Plot the graph .

The graph of the equation$x=\frac{y^2}{4}+y$of parabola is shown below .