Question

Finding the Equation of a Parabola Find an equation for the parabola that has its vertex at the origin and satisfies the given condition(s).

Focus: $F(-8,0)$

Short answer

The equation of the parabola with vertex at origin and focus $F(-8,0)$ is $y^2=-32x$.

Step-by-step solution

Step 1.Given information.

The vertex of the parabola is $\text{V(0,0)}$ and the focus is $F(-8,0)$ .

Step 2. Find the equation of the parabola.

Substituting the value of $\text{p}$in the standard form of the parabola.

Vertex of the parabola is$\text{V(0,0)}$
Focus of the parabola is$F(-8,0)$
The standard form of the focus is$F(p,0)$.
We see that,$p=-8$.

Directrix:

$\begin{array}{l}x=-p\\ x=-8\end{array}$

The standard form of the parabola is,

$x^2=4py$

Substituting the value of$p=-8$in the standard form

$\begin{array}{l}\Rightarrow y^2=4\times (-8)\times x\\ \Rightarrow y^2=-32x\end{array}$

Hence, the equation of the parabola is, $y^2=-32x$ .