Geometric Construction 6

Conics

An ellipse is the locus of a point which moves so that the sum of its distances from two fixed points (the loci) remains the same. A hyperbola is the locus of a point which moves so that the difference of its distances from two fixed points (the loci) remains the same. Construct the ellipse and hyperbola according to this definition by using the command "perpendicular bisector".

Construct the ellipse / the hyperbola as an envelope of its tangents.

Draw the pair of tangents from a given point to the ellipse / hyperbola.

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.

Construct a conic given four of its points and tangent to a given line through one of the points.

Construct a conic given a pair of tangents and their point of contact and another point of the conic.

Construct a conic given three tangents and the points of contact of two of them.

Construct a conic given four tangents and the points of contact of one of them.

Construct a conic tangent to five given lines.

Construct the deltoid as an envelope of the Simson line of a triangle.

Construct a deltoid, a triangle and an ellipse all tangent to each other.

Construct the orthopole of a triangle.

Construct four ellipses and a deltoid all tangent to each other.