SOLUTION: identify the conic by writing the equation in standard form (4y^2)-(2x^2)-4y+8x-15=0

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: identify the conic by writing the equation in standard form (4y^2)-(2x^2)-4y+8x-15=0      Log On


   

Question 721985: identify the conic by writing the equation in standard form (4y^2)-(2x^2)-4y+8x-15=0
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The process needed is Complete the Square, and you do it for the x and for the y.

%284y%5E2%29-%282x%5E2%29-4y%2B8x-15=0
4y%5E2-4y-2x%5E2%2B8x-15=0
4%28y%5E2-y%29-2%28x%5E2-4x%29-15=0
The square term to use for y is %281%2F2%29%5E2=1%2F4 and the square term to use for x is %284%2F2%29%5E2=4.

4%28y%5E2-y%2B1%2F4%29-4%281%2F4%29-2%28x%5E2-4x%2B4%29-%28-2%29%284%29=15, combined a step as well as added and subtracted the appropriate square quantities and their results.
4%28y-1%2F2%29%5E2-2%28x-2%29%5E2-1%2B8=15
4%28y-1%2F2%29%5E2-2%28x-2%29%5E2=15-7
4%28y-1%2F2%29%5E2-2%28x-2%29%5E2=8, now divide each side by 8
highlight%28%281%2F2%29%28y-1%2F2%29%5E2-%281%2F4%29%28x-2%29%5E2=1%29

HYPERLOBA.

Note that you might want to see it written as
highlight%28%28%28y-1%2F2%29%5E2%29%2F2+-%28%28x-2%29%5E2%29%2F4+=1%29