Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have $x^2+2xy-2y^2+x-4y=0$ and I have to find its canonical form, but I'm a little confused.. I'd like to understand very well what I have to do.. Can you help me, please? Thanks!

share|improve this question
1  
First of all, decide whether it is an ellipse, a hyperbola, or a parabola. This is easy. –  Siminore Sep 14 '12 at 12:06
    
May have a look into : math.stackexchange.com/questions/194535/ellipse-question –  lab bhattacharjee Sep 14 '12 at 12:23
    
@Siminore, yes it is easy! :) But then.. what do I have to do? I'd like to understand the steps needed to get the canonical form. Could you help me? –  sunrise Sep 14 '12 at 17:41
    
@labbhattacharjee I'm sorry, thank you, but my Prof doesn't like this proceeding... –  sunrise Sep 14 '12 at 18:01
    
@sunrise What are you allowed to use, then? –  Siminore Sep 15 '12 at 8:05

1 Answer 1

up vote 3 down vote accepted

You want to eliminate the term involving $xy$. The simplest way for this example is to notice that $x^2+2xy=(x+y)^2-y^2$. So we use new variables $X=x+y, Y=y$ or $x=X-Y, y=Y$. Making this substitution gives $X^2-3Y^2+X-5Y=0$, and so it is a hyperbola.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.