Equations of Conic Sections

1
Equations of Conic Sections

• Circles, Parabolas, Hyperbolas, and Ellipses

Heidi Wieland Class
of 2007 5-7-07
2
Circles

• To find an equation of a circle, use the distance
  formula.
• The circle has center C (h, k) and radius r.
• Use the equation
• (x-h)2 (y-k)2

3
Ellipses
An ellipse has a major axis a and a minor axis b.
The major axis, a, is the distance from the
center of the ellipse to the vertices. This
connects the foci. The minor axis, b, is
perpendicular to the major axis. With ellipses,
we use the equation b2a2-c2 Use the
equation x2 y2 1 a2 b2
4
Hyperbolas

• Hyperbola equations are very similar to ellipse
  equations. In a hyperbola equation, however,
  b2c2-a2.
• Use the equation
• x2 - y2 1
• a2 b2

5
Parabolas

• A parabola is the set of all points P in a plane
  that are equidistant from a fixed point F, the
  focus, and a fixed line D, the directrix. The
  line that goes through F and is perpendicular to
  D is the line of symmetry. It intersects the
  parabola at its vertex.
• Use the equation
• pX2
• Pdistance between the directrix and the vertex