Proof of Theorem 3

Theorem 3 La Hire's Theorem
Suppose that C: x^TMx=0 is a non-degenerate conic and that U and V are any points.
Then U lies on the polar of V if and only if V lies on the polar of U.

Proof
Suppose that U=[u] and that V=[v].
Then each condition is clearly equivalent to u^TMv=0.

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