# 12: Analytic Geometry

*Thumbnail: Conic sections can also be described by a set of points in the coordinate plane. Later in this chapter, we will see that the graph of any quadratic equation in two variables is a conic section. The signs of the equations and the coefficients of the variable terms determine the shape. This section focuses on the four variations of the standard form of the equation for the ellipse. An ellipse is the set of all points (x,y)(x,y) in a plane such that the sum of their distances from two fixed points is a constant. Each fixed point is called a focus(plural: foci).*