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what conic section does the following equation represent:
A hyperbola because it has two squared terms whose coefficients have OPPOSITE SIGNS when on the same side of the equation, they are the terms and .
Rule: I will use "square term" to mean either a term in x² or a term in y².
No square terms at all -- a straight line
One square term -- parabola
Two square terms whose coefficients are EQUAL when on the same side of the equation -- circle
Two square terms whose coefficients have the SAME sign when on the same side of the equation -- ellipse (the circle is a special case of the ellipse.)
Two square terms whose coefficients have OPPOSITE SIGNS when on the same side of the equation -- hyperbola.
Edwin
