What are the coordinates of these points of intersection?

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  • 1 month ago

    y²/9 - x² = 1 

    Add x² to both sides

    y²/9  = 1 + x²

    Subtract 1 from both sides

    y²/9 - 1 = x²

    -----------------------

    x² + y² = 9

    Substitute for x² 

    y²/9 - 1 + y² = 9

    Add 1 to both sides

    y²/9 + y² = 10

    Multiply both sides by 9

    y² + 9y² = 90

    10y² = 90

    Divide both sides by 10

    y² = 9

    Take the square root of both sides

    y = ±3

    --------------------------

    x² + y² = 9

    For y = +3

    x² + (3)² = 9

    x² - 9 = 9

    x² = 0

    x = 0

    -----------------------

    For y = -3

    x² + (-3)² = 9

    x² + 9 = 9

    x² = 0

    x = 0

    --------------------

    Solutions

    (0, -3) and (0, 3) <–––––––––

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