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Conic through five given points A,B,C,P,Q

The picture shows 5 points and the unique conic containing them
Move the green point at the intersection of white and cyan lines along the
magenta lines to see points on the
conic swept out by intersection of a line through P and corresponding line
through Q (this is a version of the diagram at the bottom of page 13
in Harris). Click on the Animate button to trace the conic by
automatically varying the lines through P.
You may also move A, B, C, P, Q to determine other conics.
Click on Show Pascal Hexagon to see the hexagon through 6 points on the conic
and the cyan line (the Pascal line) containing intersections of opposite sides.
Further, the conic is bijective with the set of lines through the point P,
showing that it is a rational curve.
Press "r" to reset the sketch.

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