Question

A circle that contains the point (0,7) is centered at the point ( 4.4) . Solve for the equation that defines the circle .

Answer 1

We have that the equation of the circle with center (h,k) is the following:

`(x-h)^2+(y-k)^2=r^2`

In this case, we have the following:

`\begin{gathered} (x,y)=(0,7) \\ (h,k)=(4,4) \end{gathered}`

doing the substitution on the equation and solving for r, we get::

`\begin{gathered} (0-4)^2+(7-4)^2=r^2 \\ \Rightarrow16+(3)^2=r^2 \\ \Rightarrow16+9=r^2 \\ \Rightarrow r^2=25^{} \\ \Rightarrow r=\sqrt[]{25}=5 \\ r=5 \end{gathered}`

therefore, the equation of the circle is:

`(x-4)^2+(y-4)^2=25`