Find the center and radius of x^2 + y^2 - 20x + 96 = 0?

To find the center and radius of the circle represented by the equation x^2 + y^2 - 20x + 96 = 0, we first need to rewrite the equation in standard form.

Completing the square for the x-terms, we get:
(x^2 - 20x) + y^2 = -96
(x^2 - 20x + 100) + y^2 = -96 + 100
(x - 10)^2 + y^2 = 4

Now, we can see that the equation is in the standard form of a circle:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius.

Comparing the equation to the standard form, we can see that the center of the circle is at (10, 0) and the radius is √4 = 2.

Therefore, the center of the circle is (10, 0) and the radius is 2.

Step 1: Rewrite the equation in standard form:

x^2 - 20x + y^2 = 96

Step 2: Complete the square for the x-term:

(x^2 - 20x + 100) + y^2 = 96 + 100
(x - 10)^2 + y^2 = 196

Step 3: Identify the center and radius:

Center: (10, 0)
Radius: r = sqrt(196) = 14

Therefore, the center of the circle is (10, 0) and the radius is 14.