Answer
Centre (3, -2); radius = 5;
x-intercepts are 3 + √21 and 3 - √21
y-intercepts are 2 and -6
Work Step by Step
2x² + 2y² - 12x + 8y - 24 = 0
x² + y² - 6x + 4y - 12 = 0
(x² - 6x)+ (y² + 4y) - 12 = 0
(x² - 6x)+ (y² + 4y) - 12 + 12 = 0 + 12 Add 12 to both sides.
(x² - 6x + 9)+ (y² + 4y + 4) = 12 + 13 Complete the square of each expression in parenthesis.
(x - 3)² + (y + 2)² = (5)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 = - 2 and r = 5.
The circle has center (3, - 2) and a radius of 5 units.
To find the x-intercepts, if any, let y = 0 and solve for x.
(x - 3)² + (0 + 2)² = (5)²
(x - 3)² + 4 = 25
(x -3)² + 4 - 4 = 25 - 4 Subtract 4 from both sides
(x - 3)² = 21
x - 3 = ± √21
x - 3 + 3 = ± √21 + 3
x = 3 ± √21
The x-intercepts are 3 + √21 and 3 - √21.
To find y-intercepts, if any, let x = 0 and solve for y.
(0 - 3)² + (y + 2)² = 25
9 + (y + 2)² = 25
(y + 2)² + 9 - 9 = 25 - 9 Subtract 9 from both sides.
(y + 2)² = 16
y + 2 = ± 4
If y + 2 = 4
y + 2 - 2= 4 - 2
y = 2
If y + 2 = - 4
y + 2 - 2 = - 4 - 2 Subtract 2 from both sides.
y = - 6
The y- intercepts are 2 and - 6.
