Answer
The given standard form of the equation to the set of points $\left( -2.4,\ -2.7 \right)$ that could be the epicenter of the quake which is 30 miles from the university is ${{\left( x+2.4 \right)}^{2}}+{{\left( y+2.7 \right)}^{2}}=900$.
Work Step by Step
Suppose that $\left( x,\ y \right)$ are the set of points that represent the epicenter.
And also the distance between the university and the epicenter is 30 miles. The distance formula to find the distance between the two points is shown below:
$d=\sqrt{{{\left( {{x}_{2}}-{{x}_{1}} \right)}^{2}}+{{\left( {{y}_{2}}-{{y}_{1}} \right)}^{2}}}$
Let ${{x}_{2}}=x\ ,\ {{x}_{1}}=-2.4,\ {{y}_{2}}=y\,\,\text{ and }\,\,{{y}_{1}}=-2.7$ and use the values in the distance formula as given below:
$\begin{align}
& 30=\sqrt{{{\left( x-\left( -2.4 \right) \right)}^{2}}+{{\left( y-\left( -2.7 \right) \right)}^{2}}} \\
& {{30}^{2}}={{\left( x-\left( -2.4 \right) \right)}^{2}}+{{\left( y-\left( -2.7 \right) \right)}^{2}} \\
& 900={{\left( x+2.4 \right)}^{2}}+{{\left( y+2.7 \right)}^{2}}
\end{align}$
or ${{\left( x+2.4 \right)}^{2}}+{{\left( y+2.7 \right)}^{2}}=900$
