How do you determine circle, parabola, ellipse, or hyperbola from equation #4x^2 - 9y^2 - 16x +18y -11 = 0#?

1 Answer
Nov 12, 2015

Answer:

EVERY conic section can be written with the general equation :

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

Explanation:

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)

So, in the problem stated above, since #AneB# (#4ne9#), but A and B have different signs (4 and -9), it is a hypebola !

hope that helped