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8 June, 15:02

What is the radius of the circle represented by the equation x^2 + y^2 - 6x + 4y = 12?

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  1. 8 June, 15:15
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    General formula of the circle

    (x-h) ² + (y-k) ² = r²

    We are going to use formula a² + / -2ab + b² = (a-b) ² to complete the squares and to write the equation in the general form.

    x² + y² - 6x + 4y = 12

    x² - 6x + y² + 4y = 12

    x² - 2*3x + 3² - 3² + y² + 2*2y + 2² - 2² = 12

    (x-3) ² - 9 + (y+2) ² - 4 = 12

    (x-3) ² + (y+2) ² = 12 + 13

    (x-3) ² + (y+2) ² = 25

    (x-3) ² + (y+2) ² = 5²

    This circle has center (3,-2) and radius = 5.
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