Question

I’m looking to answer question 12. and 14. Which are to use the Information provided to write the equation of each circle.

Answer 1

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:

`(x-0)^2+(y-13)^2=25`