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)

Question

asked Mar 24, 2021 155k views

1 Answer

Nuno Ferro · Answer 1 · 2021-03-29T22:57:38+0000

Answer:

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

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

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 :

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