$\"\"$

The discriminant is $\"\"$ .

Rewrite the function $\"\"$ .

The general form of the conic equation is $\"\"$ .

Identify the conic section using the discriminant of $\"\"$ .

If a circle $\"\"$ ; $\"\"$ and $\"\"$ .

If an ellipse $\"\"$ ; either $\"\"$ and $\"\"$ .

If a hyperbola $\"\"$ .

If an parabola $\"\"$ .

Here $\"\"$ .

Subustiute the values in the equation $\"\"$ .

$\"\"$

The discriminant is greater than $\"\"$ , so the conic is an hyperbola.

$\"\"$

The conic is an hyperbola.