21340Re: [EMHL] Re: Happy New Year and Nik's locus for 2013
- Jan 2, 2013Dear all,
If A'B'C' is the pedal triangle of P (instead of cevian triangle of P), and A", B", C" as before,
If A* is the homothetic of A" under h(A', k), B* and C* likewise, then the locus of P such that ABC and A*B*C* are perspective (at X) is a central cubic passing through X3 with asymptotes parallel to the altitudes of ABC and concurring on the Brocard axis, very similar to the Darboux cubic which is obtained when k = 0.
The locus of the perspector X is pK(X2, T) where
T = (-a^4+b^4+c^4)k-4 SA Sw : : , on the line X4-X69.
If k = 0, T = X69 and this is the Lucas cubic.
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