The shape and type of the conic section constructed depend upon the position of the second focus!
here's another way to look at it -
depending on the positioning of the second focus two different types of conic sections are generated
• depending on the positioning of the second...
related videos -
Constructing an Ellipse when its two foci are given
• Constructing an Ellipse when its two foci ...
constructing an ellipse when its two foci are given - 2
• constructing an ellipse when its two foci ...
the shape of the conic section transforms into a hyperbola as the position of the 2nd focus is moved outside the "Construction Circle"