Question

The center of a circle is (0,-6). The radius is 4. What is the equation of the circle? Select all that apply (look at picture)

Answer 1

`{x}^(2) + {y}^(2) + 12y + 20 = 0`

`{x }^(2) + {(y + 6)}^(2) = 16`

Explanation:

The equation of a circle with center (a,b) and radius r, is given by:

`{(x - a)}^(2) + {(y - b)}^(2) = {r}^(2)`

The given circle has centre (0,-6) and radius r=4.

We substitute these values into the formula to get:

`{(x - 0)}^(2) + {(y - - 6)}^(2) = {4}^(2)`

This implies that:

`{x }^(2) + {(y + 6)}^(2) = 16`

When we expand, we get:

`{x}^(2) + {y}^(2) + 12y + 36 = 16`

The general form is :

`{x}^(2) + {y}^(2) + 12y + 20 = 0`