Write the equation of this circle in standard form: (x-h)^2 + (y-k)^2 = r^2,
where (h,k) represents the center of the circle.
We must use the "complete the square" approach twice here:
X^2 + y^2 – 10x + 6y = 15
Rewrite this as x^2 - 10x + y^2 + 6y = 15
Complete the square of x^2 - 10x:
x^2 - 10x + 25 - 25
Complete the square of y^2 + 6y:
y^2 + 6y + 9 - 9
Then rewrite X^2 + y^2 – 10x + 6y = 15 as
x^2 - 10x + 25 + y^2 + 6y + 9 = 15 + 25 + 9
Or as (x-5)^2 + (y+3)^2 = 49
Then the equation of the circle in standard form is
(x-5)^2 + (y+3)^2 = 7^2.
The center of this circle is at (5,-3), and its radius is 7.