Question

Part 2 - Find the error(s) and solve the problem correctly.Find the equation of the circle. What is the center and radius of the circle?Be sure to show all work and explain your answer.

Answer 1

We need to find the equation of the circle using the next equation:

`x^2+y^2+8x-2y-13=0`

Then:

`x^2+8x+y^2-2y=13`

Now, we need to complete the squares :

`\begin{gathered} x^2+8x+16=(x^2+4)^2 \\ and \\ x^2-2y+1=(x^2-1)^2 \end{gathered}`

Then, we have the next expression:

`\begin{gathered} x^2+8x+16+y^2-2y+1=13+16+1 \\ Simplofy: \\ (x^+4)^2+(y-1)^2=30 \end{gathered}`

We have the form (x-h)² + (y-k)²=r²

Where (h,k) is the center and r represents the radius.

Now, the center is (-4,1)

and the radius is √30 = 5.47....