Determine the center and radius of the following circle equation:

x^2+y^2-6x-8y+24=0

Center is (3, - 4) and radius is 1

Step-by-step explanation:

Step 1: Find center and radius of the circle with equation x² + y² - 6x - 8y + 24 = 0

The standard form of the equation of a circle is x² + y² + 2gx + 2fy + c = 0, where center is (-g, - f) and radius = √g² + f² - c

By comparing the 2 equations, 2g = - 6, 2f = 8 and c = 24

⇒ g = - 6/2 = - 3

⇒ f = 8/2 = 4

⇒ c = 24

Step 2: Find center.

Center = (-g. - f) = (3, - 4)

Step 3: Find radius.

Radius = √g² + f² - c = √3² + (-4) ² - 24

= √9 + 16 - 24 = √1 = 1