Anonymous
Anonymous asked in Science & MathematicsMathematics · 6 months ago

Find the radius of a circle with the equation: x^2+y^2-14y+124=0?

geometry

9 Answers

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  • 6 months ago

    x^2 + y^2 - 14y + 124 = 0

    This isn't a circle.

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  • 6 months ago

    √(0²+(-7)²-124) = √-75 which is an invalid value for a radius on the real plane.

    Source(s): x² + y² + 2ax + 2by + c = 0 rearranges to (x+a)² + (y+b)² = a² + b² - c, a circle centred at (-a,-b) with a radius of √(a²+b²-c)
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  • Ian H
    Lv 7
    6 months ago

    x^2 + y^2 - 14y + 124 = 0

    The equation you gave, (above), was not a circle. Perhaps it should have been

    x^2 + y^2 - 14y = 124

    x^2 + y^2 - 14y + 49 = 124 + 49

    x^2 + (y - 7)^2 = 173

    Centre (0, 7) radius √(173)

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  • 6 months ago

    Ans. such circle does not exist, check out

    your problem.

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  • 6 months ago

    Complete the square in 'x' & 'y'

    Hence

    x = 0

    (y - 14/2)^2 - (14/2)^2 = 0

    ( y - 7)^2 = 196/4

    y - 7 = 14/2 = 7

    y = 14

    Hence 124 = 0^2 + 14^2=

    124 = 49

    =75 which is r^2

    r = sqrt(75) = 5sqrt(3) or 8.660....

    Hence the original eq'n is

    (x - 0)^ + ( y - 14)^2 = 75

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  • Mike G
    Lv 7
    6 months ago

    x^2+y^2-14y+49 = -124+49

    x^2+(y-7)^2 = -75

    Radius is an imaginary number

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  • DWRead
    Lv 7
    6 months ago

    The equation you've provided is not a circle. Did you mean to write

    x² + y² - 14y - 124 = 0?

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  • 6 months ago

    If that's supposed to be:

    x² + y² - 14y - 124 = 0

    then we can move the constant to the right side:

    x² + y² - 14y = 124

    Then complete the square with the y's adding 49 to both sides:

    x² + y² - 14y + 49 = 124 + 49

    Now factor the y's as a perfect square trinomial and simplify the right side:

    x² + (y - 7)² = 173

    The center of this is (0, 7) and the radius is √173

    Your equation as shown is not a circle.

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  • x^2 + y^2 - 14y = -124

    x^2 + y^2 - 2 * 7 * y = -124

    x^2 + y^2 - 2 * 7 * y + 49 = 49 - 124

    (x - 0)^2 + (y - 7)^2 = -75

    This isn't a circle.

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