Question

What are the center and radius of the circle defined by the equation x2 + y2 -6 x + 10y + 25 = 0

Answer 1

Answer:

(3,-5), radius 3

Step-by-step explanation:

Answer 2

To determine the center points and the radius of the circle, we can either graph the equation or write it in a form where the center and the radius can be easily be seen. For this, we use the second method. The form should be:

(x - h)^2 + (y-k)^2 = r^2

(h,k) represent the center and r the radius

We do as follows:
x2 + y2 -6x + 10y + 25 = 0
x2 -6x + y2 + 10y = - 25
x2 - 6x + 9 +  y2 + 10y + 25 = -25 + 9 + 25 = 9
(x - 3)^2 + (y + 5)^2 = 3^2

Therefore, the center is at ( 3,-5) and the radius is 3 units.