SOLUTION: I need the step by step process to classify this conic section using the discriminant I was sick the day of the lesson and really have no clue on how to begin I would greatly appre

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I need the step by step process to classify this conic section using the discriminant I was sick the day of the lesson and really have no clue on how to begin I would greatly appre      Log On


   



Question 723467: I need the step by step process to classify this conic section using the discriminant I was sick the day of the lesson and really have no clue on how to begin I would greatly appreciate it if you could include the equation that this problem is based on also.-
+6x%5E2-2y%5E2%2B24x%2B2y-1=0+

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The discriminant of the equation Ax%5E2+%2B+Bxy+%2B+Cy%5E2+%2B+Dx+%2B+Ey+%2B+F+=+0 is the quantity B%5E2+-+4AC.
Assuming A, B and C are not+all +0 and that degenerate cases are excluded.
Then,
if B%5E2+-+4AC+%3C+0, the graph is an ellipse or a circle
if B%5E2+-+4AC+=+0, the graph is a parabola
if B%5E2+-+4AC+%3E+0, the graph is a hyperbola
you have
6x%5E2-2y%5E2%2B24x%2B2y-1=0.....where A=6, B=0,C=-2,D=24,E=2, and F=-1
B%5E2+-+4AC=0%5E2+-+4%2A6%2A%28-2%29=-24%2A%28-2%29=48
so, B%5E2+-+4AC+%3E+0, the graph is a hyperbola
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+6x%5E2-2y%5E2%2B24x%2B2y-1%3E=0%29+