Answer:
(x + 2)^2 + (y - 5)^2 = 32 or [4√2]^2
Step-by-step explanation:
Here we have a circle with center at (-2, 5), which represents (h, k). Thus, the standard equation of a circle with center at (h, k), shown below
(x - h)^2 + (y - k)^2 = r^2 (where r represents the radius of the circle)
becomes:
(x + 2)^2 + (y - 5)^2 = r^2. We know that this circle passes through (-6, 1), so this last equation becomes:
(-6 + 2)^2 + (1 - 5)^2 = r^2, or 16 + 16 = r^2.
Then 2(16) = r^2.
Taking the square root of both sides yields r = 4√2.
The desired equation of this circle is then
(x + 2)^2 + (y - 5)^2 = 32 or [4√2]^2
