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6 March, 10:16

Convert the equation to the standard form for a hyperbola 4x^2-25y^2-8x+50y-121=0

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  1. 6 March, 10:19
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    We have that

    4x²-25y² - 8x+50y-121=0

    Group terms that contain the same variable, and move the constant to the opposite side of the equation

    (4x²-8x) + (-25y²+50y) = 121

    Factor the leading coefficient of each expression

    4 (x²-2x) - 25 (y²-2y) = 121

    Complete the square twice. Remember to balance the equation by adding the same constants to each side.

    4 (x²-2x+1) ²-25 (y²-2y+1) ²=121+4-25

    Rewrite as perfect squares

    4 (x-1) ²-25 (y-1) ²=100

    Divide both sides by the constant term to place the equation in standard form

    (4/100) (x-1) ² - (25/100) (y-1) ²=100/100

    (1/25) (x-1) ² - (1/4) (y-1) ²=1

    [ (x-1) ²]/25-[ (y-1) ²]/4=1

    the answer is

    [ (x-1) ²]/25-[ (y-1) ²]/4=1
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