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Math Help - Reduce the conic to standard form

  1. #1
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    Reduce the conic to standard form

    I have a conic equation

    36y^2+504y-4x^2+48x+1476=0

    Which I am required to write in one of the following formats:

    \frac{x^2}{a^2}+\frac{y^2}{b^2}=1

    \frac{x^2}{a^2}-\frac{y^2}{b^2}=1

    \frac{y^2}{a^2}-\frac{x^2}{b^2}=1

    y=ax^2

    y=ay^2

    I've been looking online for a guide on how to do this, but with little success so far. Perhaps any of you can help. Thanks
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  2. #2
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    Quote Originally Posted by aspotonthewall View Post
    I have a conic equation

    36y^2+504y-4x^2+48x+1476=0

    Which I am required to write in one of the following formats:

    \frac{x^2}{a^2}+\frac{y^2}{b^2}=1

    \frac{x^2}{a^2}-\frac{y^2}{b^2}=1

    \frac{y^2}{a^2}-\frac{x^2}{b^2}=1

    y=ax^2

    y=ay^2

    I've been looking online for a guide on how to do this, but with little success so far. Perhaps any of you can help. Thanks
    start by dividing every term by 4 ...

    9y^2+126y-x^2+12x+369=0

    start the process of completing the squares ...

    9(y^2+14y) - (x^2-12x) = -369

    9(y^2+14y+49) - (x^2-12x+36) = -369 +9(49) - 36

     <br />
9(y+7)^2 - (x-6)^2 = 36<br />

    divide every term by 36 ...

     <br />
\frac{(y+7)^2}{4} - \frac{(x-6)^2}{36} = 1<br />

     <br />
\frac{(y+7)^2}{2^2} - \frac{(x-6)^2}{6^2} = 1<br />
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  3. #3
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    Quote Originally Posted by aspotonthewall View Post
    I have a conic equation

    36y^2+504y-4x^2+48x+1476=0

    Which I am required to write in one of the following formats:

    \frac{x^2}{a^2}+\frac{y^2}{b^2}=1

    \frac{x^2}{a^2}-\frac{y^2}{b^2}=1

    \frac{y^2}{a^2}-\frac{x^2}{b^2}=1

    y=ax^2

    y=ay^2

    I've been looking online for a guide on how to do this, but with little success so far. Perhaps any of you can help. Thanks

    Complete the square: if t is a variable/unknown, we have that At^2\pm Bt=A\left(t\pm\frac{B}{2A}\right)^2-\frac{B^2}{4A}\,,\,\,A\neq 0

    Do this with the variables x,y and then do some algebraic order...BTW, you should get a north-south hyperbola with semiaxis 2 and 6.

    Tonio
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