Answer:
Center → (1, -3)
Radius → 5 units
Explanation:
Equation of the given circle is,
x² + y² - 2x + 6y - 15 = 0
Now convert this equation into the standard equation of the circle
x² - 2x + y² + 6y - 15 = 0
x² -2x + 1 - 1 + y² + 2(3)(y) + 9 - 9 - 15 = 0
(x² - 2x + 1) - 1 + (y² + 2(3y) + 9) - 9 - 15 = 0
(x - 1)² + (y + 3)² - 10 - 15 = 0
(x - 1)² + (y + 3)² = 25
(x - 1)² + (y + 3)² = 5²
By comparing this equation with the standard equation of the circle,
(x - h)²+ (y - k)² = r²
Where (h, k) is the center and r is the radius of the circle.
Center of the circle → (1, -3)
Radius of the circle → 5 units