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 $\left(-2,0\right)$and directix of the line $x=2$.

Short answer

The equation of a parabola is $y^2=-8x$. The points are $\left(-2,4\right)$and $\left(-2,-4\right)$. The graph of an equation is :

Step-by-step solution

Step 1. Given Information.

The given focus of an equation be$\left(-2,0\right)$and an equation of its directix of a line be$x=2$.

Step 2. Equation of a parabola.

The vertex of an equation be at $\left(0,0\right)$. The vertex is midway between the focus and the directix. Since, the focus is on the x-axis at $\left(-2,0\right)$, the equation of the parabola is f the form

role="math" localid="1646657517636" $y^2=4ax$with $a=-2$.

i.e.$y^2=-8x$.

Step 3. Latus rectum.

The points that determine the latus rectum by letting $x=-2$.

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

The points are$\left(-2,4\right)$and$\left(-2,-4\right)$.

Step 4. Graphing utility.

The graph of an equation $y^2=-8x$will be