2x² + 2y² - 12x + 8y - 24 = 0
+ 24 + 24
2x² + 2y² - 12x + 8y = 24
2x² - 12x + 2y² + 8y = 24
2x² - 12x + 18 + 2y² + 8y + 4 = 24 + 18 + 8
2(x²) - 2(6x) + 2(9) + 2(y²) + 2(4y) + 2(2) = 50
2(x² - 6x + 9) + 2(y² + 4y + 4) = 50
2(x² - 3x - 3x + 9) + 2(y² + 2y + 2y + 4) = 50
2[x(x) - x(3) - 3(x) + 3(3)] + 2[y(y) + y(2) + 2(y) + 2(2)] = 50
2[x(x - 3) - 3(x - 3)] + 2[y(y + 2) + 2(y + 2)] = 50
2(x - 3)(x - 3) + 2(y + 2)(y + 2) = 50
2(x - 3)² + 2(y + 2)² = 50
2 2
(x - 3)² + (y + 2)² = 25
25 25 25
(x - 3)²/25 + (y + 2)²/25 = 1
X-Intercept: (x - 3)²/25 + (y + 2)²/25 = 1
(x - 3)²/25 + (0 + 2)²/25 = 1
(x - 3)²/25 + (2)²/25 = 1
⁽ˣ⁻³⁾²/₂₅ + ⁴/₂₅ = 1
- ⁴/₂₅ - ⁴/₂₅
⁽ˣ⁻³⁾²/₂₅ = ²¹/₂₅
25(⁽ˣ⁻³⁾²/₂₅) = 25(²¹/₂₅)
(x - 3)² = 21
√(x - 3)² = ±√21
x - 3 = ±√21
+ 3 + 3
x = 3 ± √21
Y-Intercept: (x - 3)²/25 + (y + 2)²/25 = 1
(0 - 3)²/25 + (y + 2)²/25 = 1
(-3)²/25 + (y + 2)²/25 = 1
9/25 + (y + 2)²/25 = 1
- 9/25 - 9/25
(y + 2)²/25 = 16/25
25((y + 2)²/25) = 25(16/25)
(y + 2)² = 16
√(y + 2)² = ±√16
y + 2 = ±4
- 2 - 2
y = -2 ± 4
y = -2 + 4 or y = -2 - 4
y = 2 or y = -6
