#### Proof of Theorem 3

**Theorem 3 La Hire's Theorem**

Suppose that **C: **__x__^{T}M__x__=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__^{T}M__v__=0.