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

Answer:

${x}^{2} + {y}^{2} + 12y + 20 = 0$

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

Step-by-step 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 :

${x}^{2} + {y}^{2} + 12y + 20 = 0$