# Can someone double check my work? conics

• Nov 22nd 2006, 08:45 AM
frogsrcool
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!:confused:
• Nov 22nd 2006, 08:53 AM
earboth
Quote:

Originally Posted by frogsrcool
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!:confused:

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