Question

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?

Answer 1

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

Explanation:

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