Question

If the center of a circle is at (5,-7)and its radius is 6, complete itsequation:(x - 5)2 + (y - [?])2 = []=

Answer 1

- The formula for finding the equation of a circle is given as:

`\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ where, \\ (a,b)\text{ is the center of the circle} \\ r\text{ is the radius of the circle} \end{gathered}`

- We have been given:

`\begin{gathered} (a,b)=(5,-7) \\ r=6 \end{gathered}`

- Thus, we can write the equation of the circle as follows:

`\begin{gathered} (x-5)^2+(y-(-7))^2=6^2 \\ (x-5)^2+(y+7)^2=36 \end{gathered}`

Final Answer

The equation of the circle is

`(x-5)^2+(y-(-7))^2=36`