Math 30 Pure

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9x^2+16y^2+64y+28=0
I am supposed to convert this to standard form, but my answer doesn't make sense. One part was 9x^2/92...does that sound right?

  • Math 30 Pure -

    16 y^2 + 64 y = - 9 x^2-28
    y^2 + 4 y = (- 9 x^2-28 )/16
    y^2 + 4 y + 4 = (- 9 x^2-28 )/16 +64/16
    (y+2)^2 = (-9 x^2 + 36 )/16
    (y+2)^2 + (9/16) x^2 = 36/16
    16/36 (y+2)^2 + 9/36 x^2 = 1

    x^2/2^2 + (y+2)^2/(3/2)^2 = 1
    ellipse with center at (0,-2)
    x half axis length 2
    y half axis length = 1.5

  • Math 30 Pure -

    Shouldn't it equal zero anyway because what does Y equal?

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