ELLIPSE. CONSTRUCTION AND ORIGIN Cross section of a cone. Always as long as the portion of the cone is wide. It is always at an angle All the points lie.

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Presentation transcript:

ELLIPSE

CONSTRUCTION AND ORIGIN Cross section of a cone. Always as long as the portion of the cone is wide. It is always at an angle All the points lie in the cone End points of ellipse are the edge of a cone.

DEGENERATE CASE “the simple case” The point where the ellipse turns into a circle

APPLICATION Construction of stone and concrete bridges Orbits of the planets around the sun “whispering galleries” (stand at one part of the room and if you whisper the person at the other side can hear you)

Standard Geometry/ Algebra II FORMS

KEY WORDS TWO RADII FOCI-(distance between is c) MAJOR AXIS (a) MINOR AXIS-(b) CENTER-(h,k)

Relationships a- the distance from center to the vertex on the major axis (2a= the entire major axis) b- the distance from the center to the vertex on the minor axis (2b= the entire minor axis) c- distance between the foci to the center T-angle of translation (u,v)- new rotated form coordinate in place of (x,y)

Rotated Conic Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0 FORMS

ECCENTRICITY How round the ellipse is. c/a=e 0 1

GRAPH