Question

Finding the Equation of a Parabola

Find an equation of the parabola whose graph is shown

Short answer

The equation of parabola is $x^2=-12y$

Step-by-step solution

Step 1. Given information

Graph of parabola is given as-

Step 2. Concept used

The equation of a parabola having a vertex at origin is –

$x^2=4py$

Where, $p>0$ then parabola open upwards

$p<0$ then parabola open downwards

The directrix is the right side of $y$-axis is so, which means the focus should be negative, the parabola opens to the left and the coordinates of focus are obtained. On substituting the value of $p$ in the equation $x^2=4py$ to obtain an equation of a parabola.

Step 3. Calculation

The focus has the coordinate $(0,-3)$, so –

$p=-3$

Now, substituting the value of $p$ in equation $x^2=4py$ , we get the equation as.

$\begin{array}{l}{x}^2=4(-3)y\\ x^2=-12y\end{array}$