math homework help..algebra 1?

Question

Transform the equation x^2 + y^2 - 6x + 9y = 1 into standard form by completeing the square.?
also can someone state center radius

Answer 1

x² + y² - 6x + 9y = 1 . Rewriting a bit,
x² - 6x + y² + 9y = 1

If the coefficient of the squared term is 1 (as it is in both cases in this equation), take half of the coefficient of the linear term, square that, and add the result to both sides of the equation:

x² - 6x + (6/2)² + y² + 9y = 1 + (6/2)²
x² - 6x + 9 + y² + 9y = 10
(x - 3)² + y² + 9y = 10
(x - 3)² + y² + 9y + (9/2)² = 10 + (9/2)²
(x - 3)² + (y + (9/2))² = 121/4
(x - 3)² + (y + (9/2))² = (11/2)²

This is the equation in standard form. From this form we can read off that the center of the circle is at (3, -9/2), and the radius of the circle is 11/2.