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CONIC SECTIONS

Briana Banks
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Briana Banks

on 11 March 2013

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Transcript of CONIC SECTIONS

CONIC SECTIONS CIRCLES DEFINITION: A circle is formed by cutting a circular cone with a plane perpendicular to the symmetry axis of the cone. EQUATION: HISTORY REAL LIFE APPLICATION Ferris Wheel ELLIPSE DEFINITION: An ellipse is all points found by keeping the sum of distances from two points constant. EQUATION: HISTORY REAL LIFE APPLICATION HYPERBOLA DEFINITION: EQUATION: A hyperbola is all points found by keeping the difference of the distances from two points constant. HISTORY REAL LIFE APPLICATION Kobe Port Tower PARABOLA DEFINITION: EQUATION: HISTORY REAL LIFE APPLICATIONS REFERENCES A parabola is formed by intersecting the plane through the cone and the top of the cone. (x-h)^2 ______ a^2 (y-k)^2 b^2 + = 1 ______ (x-h)^2 + (y-k)^2 = r^2 (x-h)^2 a^2 - (y-k)^2 b^2 = 1 ______ ______ (y-k) (x-k)^2 = 4p ______ Tycho Brahe Planetarium in Copenhagen http://usiweb.usi.edu Gateway Arch: St. Louis, Missouri Roller Coaster Power Plant Quarter The ellipse was first studied by Menaechmus. Kepler, in 1602, said he believed that the orbit of Mars was oval, then he later discovered that it was an ellipse with the sun at one focus. In 1705 Halley showed that the comet, which is now called after him, moved in an elliptical orbit round the sun. http://www-history.mcs.st-and.ac.uk http://algebralab.com http://wyzant.com A special case of the hyperbola was first studied by Menaechmus. Euclid and Aristaeus wrote about the general hyperbola but only studied one branch of it while the hyperbola was given its present name by Apollonius. The parabola was studied by Menaechmus. Euclid wrote about the parabola and it was given its present name by Apollonius. Gregory and Newton considered the properties of a parabola. The study of the circle goes back beyond recorded history. The invention of the wheel is a fundamental discovery of properties of a circle. The greeks considered the Egyptians as the inventors of geometry.
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