Question

Given equation of a circle: x^2 – 4x + y^2 + 6y = 12 rewrite it in a standard form. Find its radius and coordinates of its center. Standard Form:_____

r:_____

Center:____

Answer 1

The standard form is:

• (x - h)² + (y - k)² = r², where (h, k) is the center, r is the radius

Convert the given into standard form by completing square:

• x² - 4x + y² + 6y = 12
• x² - 4x + 4 + y² + 6y + 9 = 12 + 4 + 9
• (x - 2)² + (y + 3)² = 25
• (x - 2)² + (y + 3)² = 5²

• The standard form is above.
• The center is (h, k) = (2, -3)
• The radius is r = 5