Question

Using the following equation, find the center and radius of the circle. you must show and explain all work and calculations to receive credit. be sure to leave your answer in exact form.

X^2 +y^2 +8x-2y+15 = 0

Answer 1

Center: (-4,1)

Radius: √2

Explanation:

Complete the square for both variables

`x^2+y^2+8x-2y+15=0\\x^2+8x+y^2-2y+15=0\\x^2+8x(+16)+y^2-2y+15(-14)=0+16-14\\x^2+8x+16+y^2-2y+1=2\\(x+4)^2+(y-1)^2=2`

Comparing our result with
`(x-h)^2+(y-k)^2=r^2`, then the center of the circle is
`(h,k)=(-4,1)` and our radius is
`r=√(2)`