Question

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

line of directix $x=-\frac{1}{2}$and vertex at the point$\left(0,0\right)$.

Short answer

The equation of a parabola is$y^2=2x$. The two points are$\left(\frac{1}{2},1\right)$and$\left(\frac{1}{2},-1\right)$.

The graph of an equation is

Step-by-step solution

Step 1. Given Information.

The given vertex is at the point$\left(0,0\right)$and the line of directix is$x=-\frac{1}{2}$.

Step 2. Equation of a Parabola.

A parabola whose focus is at $\left(\frac{1}{2},0\right)$and whose directix is the line $x=-\frac{1}{2}$has its vertex at $\left(0,0\right)$.The equation of a parabola is of the form as

$$\begin{gathered} y^2=4ax \\ {y}^2=2x \end{gathered}$$

where$a=\frac{1}{2}$.

Step 3. Latus Rectum.

The two points that determines the latus rectum by letting $x=\frac{1}{2}$.Then,

$$\begin{gathered} y^2=2x \\ {y}^2=2\left(\frac{1}{2}\right) \\ {y}^2=1 \\ y=\pm 1 \end{gathered}$$.

The points are$\left(\frac{1}{2},1\right)$and$\left(\frac{1}{2},-1\right)$.

Step 4. Graphing Utility.

The graph of a parabola is