# Verification of a parabola

TonyC
I would like to verify my answer please:
x^2-2xy+y^2+5x+5y=0

using the formulas b^2-4ac=0 (indicates a parabola)
b^2-4ac<0 (indicates an ellipse)
b^2-4ac>0 (indicates a hyperbola)

2^2-4(1)(1)=0
4-4=0 therefore this graph must be a parabola!

Am I correct?

## Answers and Replies

Homework Helper
It's indeed a parabola

TonyC
YIPPEE, thank

Science Advisor
Homework Helper
Gold Member
Dearly Missed
Note that your equation may be re-written as:
$$(x-y)^{2}+5(x+y)=0$$
This can be brought onto the form:
$$u=-\frac{\sqrt{2}}{5}v^{2}, u=\frac{x+y}{\sqrt{2}}, v=\frac{x-y}{\sqrt{2}}$$
where the u-v axes are 45 degrees rotated with respect to the xy axes.