You are here
Homehomogeneous equation
Primary tabs
homogeneous equation
The homogeneous equation
$f(x,\,y)=0,$ 
where the left hand side is a homogeneous polynomial of degree $r$ in $x$ and $y$, determines the ratio $x/y$ between the indeterminates. One can be persuaded of this by dividing both sides of the equation by $y^{r}$. Then the left side depends only on $x/y$ (which may be denoted e.g. by $t$).
Examples

The equation $5x+8y=0$ determines that $x/y=\frac{8}{5}$.

The equation $x^{2}7xy+10y^{2}=0$ determines that $x/y=2$ or $x/y=5$ (these values are obtained by first dividing both sides of the equation by $y^{2}$ and then solving the equation $(x/y)^{2}7(x/y)+10=0$).

The equation $2x^{3}x^{2}y6xy^{2}+3y^{3}=0$ determines that $x/y=\frac{1}{2}$ or $x/y=\pm\sqrt{3}$ (first divide the equation by $y^{3}$ and then solve $2(x/y)^{3}(x/y)^{2}6(x/y)+3=0$).
Mathematics Subject Classification
26C05 no label found26B35 no label found00A99 no label found Forums
 Planetary Bugs
 HS/Secondary
 University/Tertiary
 Graduate/Advanced
 Industry/Practice
 Research Topics
 LaTeX help
 Math Comptetitions
 Math History
 Math Humor
 PlanetMath Comments
 PlanetMath System Updates and News
 PlanetMath help
 PlanetMath.ORG
 Strategic Communications Development
 The Math Pub
 Testing messages (ignore)
 Other useful stuff
 Corrections