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Math Help - Distance between vertices

  1. #1
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    Distance between vertices

    Determine the distance D between the vertices of -9x^{2} + 18 x + 4<br />
y^{2} + 24 y - 9 = 0
     D =
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  2. #2
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    Quote Originally Posted by viet View Post
    Determine the distance D between the vertices of -9x^{2} + 18 x + 4<br />
y^{2} + 24 y - 9 = 0
     D =
    This is an hyperbola. First get it into standard form by completing the square on both the x and y terms:
    -9x^{2} + 18 x + 4<br />
y^{2} + 24 y - 9 = 0

    -(9x^{2} - 18 x) + (4y^{2} + 24y) = 9

    -9(x^2 - 2x) - 4(y^2 + 6y) = 9

    -9 ( x^2 - 2x + 1 ) + 9 + 4(y^2 + 6y + 9) - 36 = 9

    -9(x - 1)^2 + 4(y + 3)^2 = 36

    -\frac{(x - 1)^2}{4} + \frac{(y + 3)^2}{9} = 1

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

    Can you finish the problem?

    -Dan
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  3. #3
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    yeah got it thanks
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