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Mathematics
Today, 13:55
Find intercepts of: 2x^2+2y^2-12x+8y-24=0
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Haley Moran
Today, 14:11
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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
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