Question

The equation of a circle is given below.

X^2+ (y + 4)^2= 64
What is its center?
What is its radius?
If necessary, round your answer to two decimal places.
units

Answer 1

Explanation:

Given equation of circle is:

`{x}^(2) + (y + 4)^(2) = 64 \\ {(x - 0)}^(2) + {(y + 4)}^(2) = {8}^(2) \\ equating \: it \: with \\ {(x - h)}^(2) + {(y - k)}^(2) = {r}^(2) \\ we \: find: \\ - h = 0 \implies \: h = 0 \\ - k = 4\implies \: k= - 4 \\ \therefore \: center = (h \: k) \\ \red{ \boxed{\bold {\therefore \: center = (0 \: - 4)}}} \\ \\ \: \: \: \purple{ \boxed{\bold {radius \: r = 8 \: units}}}`