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Math Help - Can someone double check my work? conics

  1. #1
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    Question Can someone double check my work? conics

    use 9x^2+4y^2+18x-16y-11=0 to do the following:
    write the equation in standrad form

    9x^2+4y^2+18x-16y-11=0
    9x^2+18x+4y^2-16y=11
    9(x^2+2) +4(y^2-4y)=11
    9[(x^2+2+1)-1] +4[(y^2-4y+4)-4]=11
    9[(x+1)^2-1] +4[(y-2)^2-4]=11

    9(x+1)^2-9 +4(y-2)^2-16=11
    9(x+1)^2+4(y-2)^2=27

    9(x+1)^2+4(y-2)^2=27
    27 27 27

    (x-1)^2 + 4(y-2)^2 =1
    3 27

    the 27 is divided by4(y-2)^2

    is this right?? I think I did something wrong!
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  2. #2
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    Quote Originally Posted by frogsrcool View Post
    use 9x^2+4y^2+18x-16y-11=0 to do the following:
    write the equation in standrad form

    9x^2+4y^2+18x-16y-11=0
    9x^2+18x+4y^2-16y=11
    9(x^2+2) +4(y^2-4y)=11
    9[(x^2+2+1)-1] +4[(y^2-4y+4)-4]=11
    9[(x+1)^2-1] +4[(y-2)^2-4]=11

    9(x+1)^2-9 +4(y-2)^2-16=11
    9(x+1)^2+4(y-2)^2=27

    9(x+1)^2+4(y-2)^2=27
    27 27 27

    (x-1)^2 + 4(y-2)^2 =1
    3 27

    the 27 is divided by4(y-2)^2

    is this right?? I think I did something wrong!
    Hello, that's right.

    I'll copy your line which contains the mistake and then add the corrected line:

    9(x^2+2) +4(y^2-4y)=11
    9(x^2+2x) +4(y^2-4y)=11

    9(x+1)^2-9 +4(y-2)^2-16=11
    9(x+1)^2+4(y-2)^2-25=11
    9(x+1)^2+4(y-2)^2=27
    9(x+1)^2+4(y-2)^2=36. Divide by 36:

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

    EB
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