Question

Identify the graph of the equation without completing the squares.

3x^2 - 2y^2 + 6x + 4 = 0

Answer 1

Step 1 :

Identify the conic from its general equation :

The graph of is one of the following

1. Circle :

2. Parabola : , (either or but not both).

3. Ellipse : , ( A and C have like signs).

4. Hyperbola : , ( A and C have unlike signs).

 Step 2 :

The equation is .

Compare with the general equation .

and A,C  are having unlike signs.

The graph of the equation represents hyperbola.

Solution :

The graph of the equation represents hyperbola.