homogeneous equation

The homogeneous equation


where the left hand is a homogeneous polynomialMathworldPlanetmathPlanetmath of degree r in x and y,  determines the ratio x/y between the indeterminatesMathworldPlanetmath.  One can be persuaded of this by dividing both of the equation by yr.  Then the left depends only on x/y (which may be denoted e.g. by t).


  • The equation  5x+8y=0  determines that  x/y=-85.

  • The equation  x2-7xy+10y2=0  determines that  x/y=2  or  x/y=5  (these values are obtained by first dividing both of the equation by y2 and then solving the equation  (x/y)2-7(x/y)+10=0).

  • The equation  2x3-x2y-6xy2+3y3=0  determines that   x/y=12  or  x/y=±3 (first divide the equation by y3 and then solve  2(x/y)3-(x/y)2-6(x/y)+3=0).

Title homogeneous equation
Canonical name HomogeneousEquation
Date of creation 2013-03-22 15:14:41
Last modified on 2013-03-22 15:14:41
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 7
Author pahio (2872)
Entry type Topic
Classification msc 26C05
Classification msc 26B35
Classification msc 00A99
Related topic Variation
Related topic HomogeneousPolynomial
Related topic Equation
Related topic RegularDecagonInscribedInCircle