Final answer:
The equation of the circle derived using completing the square is (x - 3)² + (y + 5)² = 36, where the center of the circle is at (3,-5) with a radius of 6 units.
Step-by-step explanation:
To find the equation of the circle using completing the square, we need to rearrange the given equation x²+y²-6x+10y-2=0 and express it in the standard form of a circle's equation, which is (x-h)²+(y-k)²=r², where (h,k) is the center of the circle and r is its radius.
First, organize the x and y terms:
x² - 6x + y² + 10y = 2
Group the x terms and y terms:(x² - 6x) + (y² + 10y) = 2
Complete the square for x:
(x - 3)² = x² - 6x + 9
Complete the square for y:
(y + 5)² = y² + 10y + 25
Add these constants inside the equation balancing by adding the same amount to the other side of the equation:
(x - 3)² + (y + 5)² = 2 + 9 + 25
Simplify:
(x - 3)² + (y + 5)² = 36
The equation of the circle is now in standard form, where the center is (3,-5) and the radius is 6 units.