# Homework Help: Problem in conics

1. Jan 31, 2013

### Hysteria X

1. The problem statement, all variables and given/known data

The equation $x^2y^2-2xy^2-3y^2-4x^2y+8xy+12y=0$ represents??

2. Relevant equations

circle: $x^2 +y^2 = a^2$

3. The attempt at a solution
i know this has something to do with seperating out the variables but i dont seem to get the req equation

Last edited: Jan 31, 2013
2. Jan 31, 2013

### Staff: Mentor

Show us what you've tried.

3. Jan 31, 2013

### Dick

You want to try to factor it somehow. Why are there two xy terms in your expression? Check for typos.

4. Jan 31, 2013

### Hysteria X

i divided the whole term by y^2 and i seperated the y and x terms on both sides of the equation then i think the next step would be to convert into factors but how am i supposed to do that why y would be in the denominator in rhs??

5. Jan 31, 2013

### Hysteria X

sorry its $xy^2$

6. Jan 31, 2013

### Dick

Ok, then start trying to factor it. You can pull a y out right away.

7. Feb 1, 2013

### Hysteria X

$x^2y^2−2xy^2−3y^2−4x^2y+8xy+12y=0$
$y^2(x^2-2x-3)-4y(x^2-2x-3)=0$
$y-4=0$
$y=4$??? what conic is that? is it a straight line

8. Feb 1, 2013

### Dick

Yes, it's a line. It can happen. xy=1 is a hyperbola. xy=0 is two lines. That's a 'degenerate conic'. But actually since your equation is 4th degree, there's not necessarily any reason to expect it to be a conic. But y=4 isn't the whole story.

Last edited: Feb 1, 2013
9. Feb 1, 2013

### Staff: Mentor

You skipped some steps here. Write the equation above as a product instead of a difference. In the two terms above there is a common factor: x2 - 2x - 3.