Conics Equation and Circle Problem: Solving for Unknown Variables

[Hysteria X]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

i know this has something to do with seperating out the variables but i don't seem to get the req equation

 

[Mark44]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

i know this has something to do with seperating out the variables but i don't seem to get the req equation

Show us what you've tried.

 

[Dick]

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

 

[Hysteria X]

Show us what you've tried.

i divided the whole term by y^2 and i separated 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??

 

[Hysteria X]

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

sorry its $xy^2$

 

[Dick]

sorry its $xy^2$

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

 

[Hysteria X]

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

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

 

[Dick]

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

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.

 

[Mark44]

$x^2y^2−2xy^2−3y^2−4x^2y+8xy+12y=0$
$y^2(x^2-2x-3)-4y(x^2-2x-3)=0$

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.

$y-4=0$
$y=4$? what conic is that? is it a straight line