Question

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

Answer 1

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