|
Question 920285: Identify the following conic. That is, is it a circle, parabola, hyperbola or ellipse? Show why?
x^2-4y^2-4x-24y=48
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
Here's how you tell just by looking at the equation, assuming there are no xy terms:
Circle -- 2nd degree polynomial equation having both x² and y² terms with the
same COEFFICIENT when on the same side of the equation.
Parabola -- 2nd degree polynomial equation having only an x² term or a y² term
but not both.
Hyperbola -- 2nd degree polynomial equation having both x² and y² terms with
OPPOSITE SIGNS when on the same side of the equation.
Ellipse -- 2nd degree polynomial equation having both x² and y² terms with
DIFFERENT COEFFICIENTS BUT BOTH WITH THE SAME SIGN when on the same side of the
equation.
------------------------------------
x²-4y²-4x-24y=48
That's a polynomial equation having both x² and y² terms with OPPOSITE SIGNS
when on the same side of the equation. So it's a HYPERBOLA.
Edwin
|
|
|
| |
