Hello from MrBillDoesMath!
Answer:
(x+4)^2 + (y+1)^2 = 20
Discussion:
The equation of a circle with center (h,k) and radius "r" is given by
(x - h)^2 + (y-k)^2 = r^2.
As (-4, -1) is the center of the circle this equation becomes:
(x - (-4))^2 + (y - (-1))^2 = r^2 =>
(x+4)^2 + (y+1)^2 = r^2.
We need to determine the value of "r", the radius of the circle. The length of the radius is the distance between the center point and the point (-2,3) . It can be gotten using the Pythagorean theorem:
r^2 = (-4 - (-2)) ^2 + (-1 - 3)^2) = (diff of x^2 + diff of y^2)
(-4 +2) ^2 + (-4)^2 =
(-2)^2 + 16)
4 + 16
So the full equation is
(x+4)^2 + (y+1)^2 = 20
Thank you,
MrB
