solving conics
posted by saad .
Explain which conic section this equation and explain how to solve it:
12x^218y^218x12y+12=0

let's complete the square to get it into standard form
12(x^2  (3/2)x + .....)  18(y^2 + (2/3)y + ...) = 12
12(x^2  (3/2)x + 9/16)  18(y^2 + (2/3)y + 1/9) = 12 + 9/16 + 1/9
12(x  3/4)^2  18(y + 1/3)^2 = 1631/144
divide by 1631/144
(x3/4)^2/(1728/1631)  (y+1/3)^2/(2592/1631) = 1
I am sure you can determine the properties of the vertical hyperbola from there.
Check my arithmetic.