Question

Which equation describes a hyperbola?

A. 2x^2 + 2x + 2y^2 - 6y - 11 = 0
B. -6x^2 + 2x - 12y^2 - 11y = 11
C. -6y^2 + 2x - 11y = -5
D. 4y^2 + 2y - 10x^2 + 2x - 6 = 0

Thanks!

Answer 1

You should recognize certain patterns to the conic section equations.

if the signs of the x^2 and y^2 terms are opposite , then you have a hyperbola,
e.g. (your example)

If their signs are the same and their coefficients are also the same, you have a circle.
e.g. 6x^2 + 9x + 6y^2 - 4y = 123

If the signs are the same, but their coefficients are different, you have and ellipse
e.g. 6x^2 + 9x + 4y^2 - 4y = 123

if one of the square terms, either the x or the y, are missing, you have a parabola

4x^2 + 8y = 77

if both square terms are missing you have straight line.