Answer
Center (0, 2); radius = 2
No x-intercepts
The y-intercepts are 4 and 0.
Work Step by Step
3x² + 3y² - 12y = 0
x² + y² - 4y = 0 Divide both sides by 3.
x²+ (y² - 4y) = 0
x² + (y² - 4y + 4) = 0 + 4 Complete the square of each expression in parenthesis.
x² + (y - 2)² = 4
x² + (y - 2)² = (2)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 = 0, k = 2 and r = 2.
The circle has center (0, 2) and a radius of 2 units.
To find the x-intercepts, if any, let y = 0 and solve for x.
x² + (y - 2)² = ( 2)²
x² + (0 -2)² = 4
x² + 4 = 4
x² + 4 - 4 = 4 - 4 Subtract 4 from both sides.
x² = 0
x = 0
No x-intercepts.
To find y-intercepts, if any, let x = 0 and solve for y.
0² + (y - 2)² = (2)²
(y - 2)² = 4
y - 2 = ± 2
If y - 2 = 2
y - 2 + 2 = 2 + 2
y = 4
If y - 2 = - 2
y - 2 + 2 = - 2 + 2
y = 0
The y- intercepts are 4 and 0.