Question

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

A) center (0,3) and radius 4
B) center (0,-3) and radius 4
C) center (0,3) and radius 16
D) center (0,-3) and radius 16

Answer 1

Option B) center
`(0,-3)` and radius
`4`

Explanation:

we know that

The equation of the circle into center radius form is equal to

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

where

(h,k) is the center of the circle

r is the radius of the circle

In this problem we have

`x^(2) +y^(2)+6y=7`

so

convert to center radius form

Complete the square. Remember to balance the equation by adding the same constants to each side

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

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

Rewrite as perfect squares

`x^(2) +(y+3)^(2)=16`

`x^(2) +(y+3)^(2)=4^(2)`

The center is the point
`(0,-3)`

The radius is
`4` units