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For example, let ''C'' be the [[Conic section|conic]] ''ax''<sup>2</sup>+''by''<sup>2</sup>+''cz''<sup>2</sup>=0. Then dual is found by eliminating ''p'', ''q'', ''r'', and λ from the equations
:<math>X= 2\lambda ap,\,Y=2\lambda bq,\,Z=2\lambda cr,\,
The first three equations are easily solved for ''p'', ''q'', ''r'', and substituting in the last equation produces
:<math>\frac{X^2}{2\lambda a}+\frac{Y^2}{2\lambda b}+\frac{Z^2}{2\lambda c}=0.</math>
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