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Math Help - HELPP! minor axis of ellipse

  1. #1
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    HELPP! minor axis of ellipse

    How would i go about finding the minor axis of the ellipse:
    4x^2+y^2-32x+6y+57=0
    Thanks
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  2. #2
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    complete the square for both x and y ...

     4x^2+y^2-32x+6y+57=0

    4x^2 - 32x + y^2 + 6y = -57

    4(x^2 - 8x) + y^2 + 6y = -57

    4(x^2 - 8x + 16) + y^2 + 6y + 9 = -57 + 64 + 9

    4(x - 4)^2 + (y + 3)^2 = 16

    \frac{(x-4)^2}{4} + \frac{(y+3)^2}{16} = 1

    \frac{(x-4)^2}{2^2} + \frac{(y+3)^2}{4^2} = 1

    the last equation contains information that the length of the semi-minor axis is 2.
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  3. #3
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    Why did you add 64 to the right side?
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    Quote Originally Posted by emetty90 View Post
    Why did you add 64 to the right side?
    because in the expression 4(x^2 - 8x + 16) on the left side of the equation, the 4 distributes to the added 16, resulting in an extra 64 on the left side, which must be balanced on the right side to maintain the equality.
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