# Equation is a parabola with a vertical axis of symmetry

1. Feb 24, 2005

### gillgill

Determine the restrictions on the constants A, C and E such that the following equation is a parabola with a vertical axis of symmetry.
Ax^2+Cy^2+x+Ey=0

a) A=0, C cannot=0, E cannot=0
b) A=0, C cannot=0, E=0
c) A cannot=0, C=0, E=0
d) A cannot=0, C=0, E cannot=0

i know that A cannot=0 and C=0....how about the x and y...what do they have to do with axis of symmetry?

2. Feb 24, 2005

### Galileo

Here's how you should not do it (I think):
If C is zero you can immediately see you have the equation of a parabola with a vertical axis of symmetry. (This eliminates two answers)
Suppose c) is the answer. It's obvious you don't have a parabola.
So one answer remains.

BTW: A parab. with a vertical axis of symmetry has the form y=a(x-b)^2+c

Last edited: Feb 24, 2005