$\"\"$

Identifying the conics without completing the squares.

Standard form of conic equation is $\"\"$ .

(a) Defines a parabola if $\"\"$ .

(b) Defines an ellipse if $\"\"$ and $\"\"$ .

(d) Defines a hyperbola if $\"\"$ .

$\"\"$

The equation is $\"\"$ .

Compare equation with standard form and write the coefficient.

Here $\"\"$ and $\"\"$ .

Therefore $\"\"$ .

Since $\"\"$ the equation defines a Hyperbola.

$\"\"$

The equation is a Hyperbola.