1. ## Classify an equation

how do i tell if an equation is a circle, parabola, an ellipse, or hyperbola?

an example is 5y^2-9y-12x^2-3x+6=0

what do i look at to determine its geometry?

2. Originally Posted by vanessa123
how do i tell if an equation is a circle, parabola, an ellipse, or hyperbola?

an example is 5y^2-9y-12x^2-3x+6=0

what do i look at to determine its geometry?
$Ay^2 - Bx^2$ ... hyperbola

$Ay^2 + Bx^2$ ... ellipse (circle if $A = B$)

$Ay \pm Bx^2$ or $Ay^2 \pm Bx$... parabola

3. Originally Posted by vanessa123
how do i tell if an equation is a circle, parabola, an ellipse, or hyperbola?

an example is 5y^2-9y-12x^2-3x+6=0

what do i look at to determine its geometry?
Since the leading factors of the squares are different (value and sign) and there aren't any summands containing $x \cdot y$ , this equation describes a hyperbola.

If the axes of the conic section are parallel to the coordinate axes, you can determine the kind of conic by:

1. The leading factors of the squares are both positive and equal: It's a circle.

2. The leading factors of the squares are positive but unequal: It's an ellipse.

3. The leading factors of the squares are different in value and sign: It's a hyperbola.

4. ok well i cant figure out if 21x^2+24xy-11y2=375 is a hyperbola or an ellipse because when i graphed it ...it ALMOST formed an ellipse but there was a gap that seperated it.

5. Originally Posted by vanessa123
ok well i cant figure out if 21x^2+24xy-11y2=375 is a hyperbola or an ellipse because when i graphed it ...it ALMOST formed an ellipse but there was a gap that seperated it.
The gap will be an artefact of the resolution of the calculator's graphics (number and size of pixels).

6. Originally Posted by mr fantastic
The gap will be an artefact of the resolution of the calculator's graphics (number and size of pixels).
im sorry i still dont quite understand? so is it an ellipse? because it sure does look like one, the only thing that is causing me to second guess my self is the gaps.

7. graph of $21x^2+24xy-11y^2=375$ ...

8. Originally Posted by skeeter
graph of $21x^2+24xy-11y^2=375$ ...
Indeed: http://www.wolframalpha.com/input/?i...1y%5E2+%3D+375.

That's what I get for taking things on face value and not checking ....