Answer:
The center of the circle is (3, -4)
The diameter of the circle is 2
Explanation:
The given equation of the circle is x² - 6·x + y² + 8·y = 24
The general form of the equation of a circle is x² + y² + 2·g·x + 2·f·y + c = 0
The center of the circle = (-g, -f)
The radius of the circle = √(g² + f² - c)
By comparing the given equation of the circle with the general form of the equation of a circle, we have;
2·g = -6, 2·f = 8, and c = 24
From 2·g = -6, we get;
∴ g = -6/2 = -3
g = -3
from 2·f = 8, we get;
∴ f = 8/2 = 4
f = 4
Therefore;
The center of the circle, (-g, -f) = (-(-3), -4) = (3, -4)
The center of the circle = (3, -4)
The radius of the circle, r = √(g² + f² - c) = √((-3)² + 4² - 24) = 1
The diameter of the circle, d = 2×r = 2 × 1 = 2
The diameter of the circle = 2.