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Math Help - 9y^2 + 7x^2 + 35 = 8x - 2x^2 - 36y find centre and radius?

  1. #1
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    9y^2 + 7x^2 + 35 = 8x - 2x^2 - 36y find centre and radius?

    rearrange this equation to show the centre-radius form of the equation of a circle. State the coordinates of the center and the radius of the circle

    9y^2 + 7x^2 + 35 = 8x - 2x^2 - 36y

    So far i have...

    9y^2 + 7x^2 + 35 = 8x - 2x^2 - 36y

    9x^2 - 8x + 9y^2 + 36y + 35 = 0

    x^2 - (8/9)x + y^2 + 4y = -35/9

    just a bit stuck now....
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  2. #2
    Senior Member Stroodle's Avatar
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    Hi,

    You need to complete the square for both x and y:

    9x^2-8x+9y^2+36y+35=0

    9(x^2-\frac{8}{9})+9(y^2+4y)+35=0

    9\left [ (x-\frac{4}{9})^2-\frac{16}{81}\right ]+9\left [(y+2)^2-4\right ]+35=0

    9(x-\frac{4}{9})^2-\frac{16}{9}+9(y+2)^2-36+35=0

    Can you take it from there?
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  3. #3
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by youmuggles View Post
    rearrange this equation to show the centre-radius form of the equation of a circle. State the coordinates of the center and the radius of the circle

    9y^2 + 7x^2 + 35 = 8x - 2x^2 - 36y

    So far i have...

    9y^2 + 7x^2 + 35 = 8x - 2x^2 - 36y

    9x^2 - 8x + 9y^2 + 36y + 35 = 0

    x^2 - (8/9)x + y^2 + 4y = -35/9

    just a bit stuck now....
    9y^2 + 7x^2 + 35 = 8x - 2x^2 - 36y

    2x^2 -8x+ 9y^2 + 36y + 7x^2 + 35 = 0

    9x^2 - 8x + 9y^2 +36y +36 -1 = 0

    x^2 - \frac{8x}{9} + y^2 + 4y + 4 - \frac{1}{9} = 0

    x^2 - \frac{8x}{9} + (y+2)^2= \frac{1}{9}

    x^2 - \frac{8x}{9} +({\frac{4}{9}})^2 + (y+2)^2= \frac{1}{9}+ {{\frac{16}{81}}^2}

    (x- {\frac{4}{9}})^2 + (y+2)^2 = \frac{25}{81}

    (x- {\frac{4}{9}})^2 + (y+2)^2 = (\frac{5}{9})^2

    Compare the above equation with the equation of a circle, that is,

    (x-h)^2 + (y-k)^2 = r^2

    you have

    center = (h,k) = ({\frac{4}{9}}, -2)

    radius = r = \frac{5}{9}
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