How do you know if the conic section #x^2 -9y^2 +36y -45= 0# is a parabola, an ellipse, a hyperbola, or a circle?

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Answer 1 · 2015-11-12T16:15:11

Look at the coefficients on #x^2 and y^2#

The coefficient on #x^2 = 1# and the coefficient on #y^2 = -9#.

If the coefficients are different and also different signs (+ or -), then it must be hyperbola.

Detailed Explanation:

EVERY conic section can be written with the general equation :

#Ax^2+By^2+Cx+Dy+E=0#

Here is how you distinguish the various conic sections from the coefficients in the general equation:

circle : #A=B#

ellipse : #AneB# but A and B both have the SAME sign (+ or -)

hyperbola : #AneB# but A and B both have DIFFERENT signs

parabola : either A or B equals 0 (only one squared term in the equation)

hope that helped