An ellipse is a collection of all points in a plane which the sum of two fixed points is called the foci a constant.

Using the distance formula, it can be determined that the equation of the ellipse is the following.

$$\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ b^{ 2 } } =1\quad where\quad a\quad>\quad b\quad>\quad 0\quad and\quad { b }^{ 2 }={ a }^{ 2 }-{ c }^{ 2 }$$