Dual curve: Difference between revisions

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Equations: Xp+Yq+Zr=0 is not even in the tangent space. (as a counter-example, take a circle x^2+y^2+1=0). it's not clear what this equation means, or where it comes from. either justify, or give a reference. thanks.
Reverted 1 edit by 66.30.119.105 (talk): See talk page. (TW)
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:<math>X=\lambda \frac{\partial f}{\partial x}(p, q, r),\,Y=\lambda \frac{\partial f}{\partial y}(p, q, r),\,Z=\lambda \frac{\partial f}{\partial z}(p, q, r).</math>
 
Eliminating ''p'', ''q'', ''r'', and λ from these equations, along with ''f(p,q,r)=0Xp''+''Yq''+''Zr''=0, gives the equation in ''X'', ''Y'' and ''Z'' of the dual curve.
 
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