10.5 Parametric Equations & Polar Coordinates
Conic Sections: Overview
Parabola represents set of points in a plane that are equidistant from a fixed point F called the focus and
the directrix which is a fixed line.
The point halfway between the focus and the directrix lying on the parabola is called the vertex.
The line through the focus perpendicular to the directrix is called the axis of the parabola.
For a parabola with focus at ( ) and directrix is , or
If the vertex is other than the origin but at ), then the equation of the parabola is
( ) ( ) if it opens upward or downward, and if the parabola opens sideways, the
equation is in the form of ( ) ( )
Set of points in a plane where the sum of the distance from two fixed points called the foci is constant.
When the foci and vertices are located on the -axis, then the equation of ellipse is where
has foci( )and vertices ( ) where
When the foci and vertices are located on the -axis, then the equation of ellipse is