Answer
Center(3, -1); radius = 1
x-intercept = 3
No y-intercept
Work Step by Step
x² + y² - 6x + 2y + 9 = 0
(x² - 6x)+ (y² + 2y) + 9 = 0
(x² - 6x)+ (y² + 2y) + 9 - 9 = 0 - 9 Subtract 9 from both sides.
(x² - 6x + 9)+ (y² + 2y + 1) = - 9 + 10 Complete the square of each expression in parenthesis.
(x - 3)² + (y + 1)² = (1)²
Compare this equation with the equation (x - h)² + (y - k)² = r².
The comparison yields the information about the circle. We see that h = 3, k = - 1 and r = 1.
To find the x-intercepts, if any, let y = 0 and solve for x.
(x - 3)² + (0 + 1)² = (1)²
(x - 3)² + 1 = 1
(x -3)² + 1 - 1 = 1 - 1 Subtract 1 from both sides.
(x - 3)² = 0
x - 3 = 0
x - 3 + 3 = 0 + 3
x = 3
The x-intercept is 3.
To find y-intercepts, if any, let x = 0 and solve for y.
(0 - 3)² + (y + 1)² = 1
9 + (y + 1)² = 1
(y + 1)² + 9 - 9 = 1 - 9 Subtract 9 from both sides.
(y + 1)² = - 8
y + 1 = ± √(-8) not real
No real y-intercept exists.
