Answer:
The center of this circle is (5, -4) and the radius is 1.
Step-by-step explanation:
First regroup these terms according to x and y :
x^2 - 10x + y^2 + 8y = -40
Next, complete the square for x^2 - 10x: x^2 - 10x + 5^2 - 5^2.
and the same for y^2 + 8y: y^2 + 8y + 16 - 16
Substituting these results into x^2 - 10x + y^2 + 8y = -40, we get:
x^2 - 10x + 5^2 - 5^2 y^2 + 8y + 16 - 16 = -40.
Next, rewrite x^2 - 10x + 25 and y^2 + 8y + 16 as squares of binomials:
Then x^2 - 10x + 5^2 - 5^2 y^2 + 8y + 16 - 16 = -40 becomes:
(x - 5)^2 + (y + 4)^2 - 25 - 16 = -40, or:
(x - 5)^2 + (y + 4)^2 = 1
This equation has the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius. Matching like terms, we get h = 5, k = -4 and r = 1.
The center of this circle is (5, -4) and the radius is 1.
