Answer:
Center: (2, 3)
Radius: 2
Step-by-step explanation:
Recall that in the equation of a circle,
(x - h)² + (y - k)² = r²,
the center is (h, k), and the radius is r.
We need to manipulate the given equation into the form of the equation of a circle shown above. We need to complete the square in x and in y.
4x² + 4y² - 16x - 24y + 36 = 0
4 is a common factor of all terms. Divide all terms by 4.
x² + y² - 4x - 6y + 9 = 0
Separate the x terms and the y terms. Subtract 9 from both sides. Leave blanks for completing the square in x and in y.
x² - 4x + ___ + y² - 6y + ___ = -9
Complete the squares in x and y. Add equal constants to the right side.
x² - 4x + 4 + y² - 6y + 9 = -9 + 4 + 9
Change each trinomial into the square of a binomial.
(x - 2)² + (y - 3)² = 2²
Center: (2, 3)
Radius: 2
