Originally Posted by

**quikwerk** Here is a question that I believe that I might have worked out partially, but I have one small sticking point that is really throwing me.

The question:

Identify the following conic. That is, is it a circle, parabola, hyperbola, or ellipse?

Show why.

Equation:

$\displaystyle x^2-4y^2-4x-24y=48$

My answer so far:

$\displaystyle x^2-4y^2-4x-24y=48$ can be identified as a hyperbola by executing the following steps:

Rearrange the terms:

[Math](x^2-4c+a)+(-4y^2-24y+b)~48-a+b[/tex]

Complete the square:

(this is where my problem lies, I'm not quite sure that my result is correct.)

(x^2-4c+1)-4(y^2+6t+4)=48+1-16