1 Answer

Cornuz · Answer 1 · 2023-07-16T18:41:43+0000

Explanation

We are given the following information:

$\begin{gathered} Center(a,b)\to(0,13) \\ Area=25\pi \end{gathered}$

We are required to determine the equation of the circle with the information above.

The standard equation of a circle is of the form:

$\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ where \\ (a,b)\to(0,13) \end{gathered}$

Next is to determine the value of the radius as follows:

$\begin{gathered} Area=25\pi \\ Area=\pi r^2 \\ 25\pi=\pi r^2 \\ r^2=25\Rightarrow r=5 \end{gathered}$

Therefore, the equation of the circle is:

$\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ (x-0)^2+(y-13)^2=25 \end{gathered}$

Hence, the equation of the circle is:

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