Question

The equation of a circle is x 2 + y 2 + 6 y = 7 x 2 + y 2 + 6 ⁢ y = 7 . What are the coordinates of the center and the length of the radius of the circle?

Answer 1

Vertex: (0,-3)

Radius: 4

Explanation:

Complete the square

`x^2+y^2+6y=7\\\\x^2+y^2+6y+9=7+9\\\\x^2+(y+3)^2=16`

The equation of a circle takes the form of
`(x-h)^2+(y-k)^2=r^2` where its center is
`(h,k)` and its radius is
`r`.

Hence, the vertex is
`(0,-3)` and the radius is
`4`.