Question

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

9x^2 + 4y^2 - 18x + 16y - 119 = 0

Answer 1

Step 1 :

Classifying 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 .

and A,C  are having like signs.

The graph of the equation represents an ellipse.

Solution :

The graph of the equation represents an ellipse.