SOLUTION: put the following conic section into standard form y^2+2y+12x+25=0 y+12x-2x^2=16 9x^2-18x+4y^2=27 x^2=y^2+1

Algebra ->  Circles -> SOLUTION: put the following conic section into standard form y^2+2y+12x+25=0 y+12x-2x^2=16 9x^2-18x+4y^2=27 x^2=y^2+1      Log On


   

Question 181800: put the following conic section into standard form
y^2+2y+12x+25=0
y+12x-2x^2=16
9x^2-18x+4y^2=27
x^2=y^2+1
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
y^2+2y+12x+25=0
y+12x-2x^2=16
9x^2-18x+4y^2=27
x^2=y^2+1
:
most all of these just involve completing the square and recognizing what kind of conic shape it is
:
1)y%5E2%2B2y%2B12x%2B25=0
:
%28y%5E2%2B2y%2B1%29-1%2B12x%2B25=0
:
%28y%2B1%29%5E2%2B12x%2B24=0--->12x=-%28y%2B1%29%5E2-24-->highlight%28x=%28-1%2F12%29%28y%2B1%29%5E2-2%29
:
2)y=2x%5E2-12x%2B16--->y=2%28x%5E2-6x%2B9%29%2B16-9%282%29
:
highlight%28y=2%28x-3%29%5E2-2%29
:
3)9%28x%5E2-2x%2B1%29-1%289%29%2B4y%5E2=27
:
9%28x-1%29%5E2%2B4y%5E2=36
:
highlight%28%28x-1%29%5E2%2F4%2By%5E2%2F9=1%29
:
4)highlight%28x%5E2-y%5E2=1%29