An ellipse with axes on Ox and Oy is defined by two points A and B.
Condition for possibility and uniqueness of this ellipse ? Solution
Find (construct) a point C on this ellipse such as triangle ABC has maximal area.
Conversely, given any point P on the plane, find (construct) two points M and N on this ellipse
such as area of PMN maximum
What do you think about the problem on a parabola or hyperbola ?