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8 November, 13:55

Find intercepts of: 2x^2+2y^2-12x+8y-24=0

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  1. 8 November, 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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