Conic Sections Conic sections are the intersection of a plane with a double cone: Circles, Parabolas, Ellipses & Hyperbolas

Circle ©National Science Foundation

Circle A circle is a set of points in a plane that are equidistant from a fixed point (center) in the plane…. –Radius = fixed distance between any point on the circle and the center of the circle

Parabolas © Long Island Fountain Company

Parabola A parabola is the set of all points in a plane equidistant from a fixed point (focus) and a fixed line in the plane (directrix). Focus Directrix d d

Ellipse © Jill Britton, September 25, 2003 Statuary Hall in the U.S. Capital building is elliptic. It was in this room that John Quincy Adams, while a member of the House of Representatives, discovered this acoustical phenomenon. He situated his desk at a focal point of the elliptical ceiling, easily eavesdropping on the private conversations of other House members located near the other focal point.

Ellipse An ellipse is a set of all points in a plane whose distances from two fixed points (foci) in a plane have a constant SUM.

Hyperbola The huge chimney of a nuclear power plant has the shape of a hyperboloid, as does the architecture of the James S. McDonnell Planetarium of the St. Louis Science Center. © Jill Britton, September 25, 2003

Hyperbola A hyperbola is a set of all points in the plane whose distance from two fixed points (foci) in the plane have a constant DIFFERENCE. d1d1 d1d1 d2d2 d2d2

Where are the Hyperbolas? A sonic boom shock wave has the shape of a cone, and it intersects the ground in part of a hyperbola. It hits every point on this curve at the same time, so that people in different places along the curve on the ground hear it at the same time. Because the airplane is moving forward, the hyperbolic curve moves forward and eventually the boom can be heard by everyone in its path. © Jill Britton, September 25, 2003