Question

Finding the Equation of a Parabola Find an equation of the parabola whose graph is shown.

Short answer

The equation of parabola for the graph is - $y^2=8x$

Step-by-step solution

Step 1. Given information.

The graph of parabola

Step 2. The equation of the parabola for the graph.

The directrix is the left side of y-axis is so, which means the focus should be positive, the parabola opens to the right and the coordinates of focus are obtained as(p,0).

On substituting the value of p in the equation $y^2=4px$to obtain an equation of a parabola

The graph for the parabola is –

The equation of directrix is -

$x=-2$

The coordinate of focus will be(p,0), so p=2.

Now, substituting the value of p in equation $y^2=4px$, we get the equation as –

$\begin{array}{l}{y}^2=4\left(2\right)x\\ \Rightarrow y^2=8x\end{array}$