Center with the equation x² - 10x + y² + 6y - 30 = 0 is (5, -3) and the radius is 8 units.
Circle with the given center and radius:
- Equation of a circle with the center (h, k) and radius 'r' is given by,
(x - h)² + (y - k)² = r²
Here, Center of the circle → (h, k)
Radius of the circle → r units
Given equation of the circle in the question is,
x² - 10x + y² + 6y - 30 = 0
Convert this equation to the standard equation of the circle.
x² - 2(5x) + y² + 2(3y) - 30 = 0
[x² - 2(5y) + 5²] - 5² + [y² + 2(3y) + 3²] - 3² = 30
(x - 5)² - 25 + (y + 3)² - 9 = 30
(x- 5)² + (y + 3)² = 64
(x- 5)² + (y + 3)² = 8²
Therefore, center of the circle is (5, -3) and radius of the circle is 8 units.
Learn more to find the center and the radius of a circle here,
https://brainly.com/question/10543303?referrer=searchResults
