SOLUTION: How do i identify the following equation as that of a line, a circle, an ellipse, a parabola, or a hyperbola. ex:3y2 - x = 0

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: How do i identify the following equation as that of a line, a circle, an ellipse, a parabola, or a hyperbola. ex:3y2 - x = 0      Log On


   

Question 315263: How do i identify the following equation as that of a line, a circle, an ellipse, a parabola, or a hyperbola.
ex:3y2 - x = 0
Found 2 solutions by Fombitz, solver91311:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
3y%5E2+-+x+=+0
x=3y%5E2
One variable is linear, the other has a power of 2.
These are signs of a parabola.
+graph%28+300%2C+300%2C+-2%2C+12%2C+-6%2C+6%2C+sqrt%28x%2F3%29%2C+-sqrt%28x%2F3%29%29+

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


If it has an term OR a term but NOT both, then it is a parabola.

If it has both and terms AND...

... the coefficients on the and terms are equal, you have a circle.

... the coefficients on the and terms are not equal, but the signs are the same (i.e. both plus or both minus) you have an ellipse.

... the coefficients on the and terms are not equal, and the signs are different, you have a hyperbola.

The example given is a parabola.

John