Dear Sung Hyun,

Let P = (p q r) as row matrix in barycentrics

and a line passing through P meets the conic at the

points P1 = (p1 q1 r1) and P2 = (p2 q2 r2).

The tangent at P1 is the line (x y z)MP1^t = 0

The tangent at P2 is the line (x y z)MP2^t = 0

and let Q = (p' q' r') be their intersection point.

We must have

(p' q' r')MP1^t = 0 and (p' q' r')MP2^t = 0.

The line (p' q' r')MR^t = 0 where R = (x y z)

is satisfied by P1, P2 and hence must be satisfied

by P also.This means that (p' q' r')MP^t = 0

and since the locus of Q is the polar of P

this locus must be the line (x y z)MP^t = 0

which means that the coefficients of the polar are MP^t.

Best regards

Nikos Dergiades

> Dear all,

>

> Can anyone tell me why polar of point P with respect to

> conic M is MP^T?

>

> Regards,

> Sung Hyun

>