Lemma
Suppose that C is a p-conic, and P is a p-point.
Then P lies on its polar with respect to C if and only if P is on C.
proof
Suppose that C has equation xTMx = 0.
If P = [p], the the polar of P is L : pTMx = 0.
Hence, P is on L if and only if pTMp = 0, i.e. P is on C.
|
|