Convert the general form equation of the circle into the standard form: x2 + y2 + 6x - 10y - 15 = 0

Step 1: Group the x terms and y terms together in the equation.

x² + 6x + y² - 10y = 15

Step 2: Complete the square for the x terms and the y terms.

To complete the square, take the coefficient of the x or y term, divide by 2, and square it.

For the x terms: (6/2)² = 9 For the y terms: (-10/2)² = 25

Add these values to both sides of the equation.

(x² + 6x + 9) + (y² - 10y + 25) = 15 + 9 + 25

Step 3: Rewrite the equation, factoring the x terms and y terms.

(x + 3)² + (y - 5)² = 49

This is the standard form equation of the circle. The center of the circle is at (-3, 5) and the radius is √49 = 7.