# When does Ax2 + Cy^2 + Dx + Ey + F = 0 represent a parabola

1. Jun 6, 2005

### gillgill

1. Determine the restrictions on the constants A, C and D so that Ax^2+Cy^2+Dx+Ey+F=0 represents a parabola that opens to the left.
I know that A=0, how do u know if CD>0 or CD<0..........??

2. The equation Ax^2+By^2+Cy=0 represents an ellipse. If 0<A<B<C, then the vertices of the ellipse are on
a line parallel to the y-axis or a line parallel to the x-axis????

3. Determine the restrictions on the constants, A, C and E such that the following equation is a parbola with a vertical axis of symmetry. Ax^2+Cy^2+x+Ey=0
i know that A can't =0 and C=0...
how can u tell if E=0 or not....???

Thanks.

2. Jun 6, 2005

### Berislav

1. What is the most general form of the equation for a parabola? Write it implicitaly and compare to the restrictions you have.
What condition must be met for the parabola to open to the left?

2. What are the vertices of an ellipse?

3. Again the same as in 1. What does it mean that it's axis of symmetry is vertical? Imagine such a parabola.

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