rectangular hyperbola chords part 1
by OronSH, Apr 9, 2024, 8:01 PM
Let 
be a rectangular hyperbola with center 
, and let 
be a chord of with midpoint 
. Prove that:
The pole of with respect to lies on line 
.
Since
the polar of passes through the point at infinity along 
and pole polar duality shows that the line through and the pole of 
is the polar of a point at infinity, which clearly must pass through 
be a rectangular hyperbola with center 
, and let 
be a chord of with midpoint 
. Prove that:The pole of
with respect to lies on line 
.Since
the polar of passes through the point at infinity along 
and pole polar duality shows that the line through and the pole of 
is the polar of a point at infinity, which clearly must pass through 
May 2025
April 2025