Verification of a parabola

  • Thread starter TonyC
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  • #1
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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

  • #2
TD
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It's indeed a parabola :smile:
 
  • #3
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YIPPEE, thank
 
  • #4
arildno
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Note that your equation may be re-written as:
[tex](x-y)^{2}+5(x+y)=0[/tex]
This can be brought onto the form:
[tex]u=-\frac{\sqrt{2}}{5}v^{2}, u=\frac{x+y}{\sqrt{2}}, v=\frac{x-y}{\sqrt{2}}[/tex]
where the u-v axes are 45 degrees rotated with respect to the xy axes.
 

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