Conics
Illustrate Pascal's Mystic Hexagram Theorem for a Circle: The points 12, 23, 31 of the intersection of the three pairs of opposite sides 1'2 and 12', 2'3 and 23', 3'1 and 13' of a hexagon 12'31'23' inscribed in a circle lie on a line. 
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Construct the conic passing through five given points. 
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Construct the conic passing through four given points and tangent to a given line which contains one of the points. 
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Given three points and two lines each containing one of the
points, construct the conic passing through the three points and
tangent to the lines at the given points. 
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Illustrate Brianchon's Theorem for a Circle: If a hexagon is circumscribed about a circle, the three joining pairs of opposite vertices are concurrent. 
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Construct the conic tangent to five given lines. 
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Construct the conic tangent to four given lines and passes through a point on one of them. 
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Construct the conic tangent to three given lines and passes
through two points on two of them.

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Construct the ellipse tangent to two fixed circles and their external common tangents. 