2 History of Conics Appolonius of Perga, great mathematician, was one of the first to study conic sections. He was the first to show all three curves. The early Greek astronomers thought that the planets orbited in a circular motion, however, Johannes Kepler was an astronomer who discovered the orbits of the Earth and other planets are other conic sections (i.e. ellipses). Newton’s analysis showed that the possible orbits are figures known as conic sections.

Gravitational Orbits Most planets have elliptical orbits. Venus, however, has such a small orbit that it appears to be circular. Comets have either elliptical or parabolic orbits. Comets with parabolic orbits pass the sun once and leave the Solar System. When two stars pass each other it results in a hyperbolic shape. ellipse hyperbola parabola circle

Conic Sections can be found all around us. Structures Mirrors Satellite Dishes Orbit Paths Etc… Can you think of any more?

What happened when you cut your cone? First resulting shape: Circle Second resulting shape: Ellipse Third resulting shape: Parabola Fourth resulting shape: Hyperbola

How can we define a circle? Circle: a closed plane curve, every point of which is equidistant from a fixed point within the curve According to Webster

How can we define an ellipse? Ellipse:a closed plane curve generated by a point moving in such a way that the sums of its distances from two fixed points is a constant : a plane section of a right circular cone that is a closed curve According to Webster

How can we define a parabola? Parabola: a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line According to Webster

How can we define a hyperbola? Hyperbola:a plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant According to Webster

References Conic Lesson Plan Power Point Background Information Historical View of Conic Sections Occurrence of the Conics Newtonian Gravitation and the Laws of Keplar Drawing the Paths and Planets Orbits Lesson/orbits_lesson_series.html