Answer
Center (-2, 0); radius = 2
The x-intercepts are - 4 and 0
No y-intercepts
Work Step by Step
2x² + 8x + 2y² = 0.
x² + 4x + y² = 0 Divide both sides by 2.
(x² + 4x)+ y² = 0
(x² + 4x + 4) + y² = 0 + 4 Complete the square of each expression in parenthesis.
x + 2)² + y² = 4
(x + 2)² + y² = (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 = - 2, k = 0 and r = 2.
The circle has center (-2, 0) and a radius 2 of units.
To find the x-intercepts, if any, let y = 0 and solve for x.
(x + 2)² + y² = (2)²
(x + 2)² + 0 = 4
(x + 2)² = 4
(x + 2) = ± 2
If x + 2 = 2
x + 2 - 2 = 2 - 2 Subtract 2 from both sides.
x = 0
If x + 2 = - 2
x + 2 - 2 = - 2 - 2 Subtract 2 from both sides.
x = - 4
The x-intercepts are - 4 and 0.
To find y-intercepts, if any, let x = 0 and solve for y.
(0 + 2)² + y² = (2)²
4 + y² = 4
y² + 4 - 4 = 4 - 4 Subtract 4 from both sides.
y² = 0
y² = 0
y = 0
No y- intercepts.
