13. The graph of 9x2 54x + 4y2 + 16y + 61 = 0 is

A.a circle with radius 6

B.a hyperbola centered at (2,3)

C. a hyperbola centered at (3,-2)

D.an ellipse centered at (2,3)

E. an ellipse centered at (3,-2)

 

Solution: The answer is E

Use completing the square method, to rewrite the given equation, as follows:

Which can now be recognized as the equation of an ellipse centered at (3,-2).