Conic Sections Examples

Share this page to google classroom the following diagram shows how to derive the equation of circle x h 2 y k 2 r 2 using pythagorean theorem and distance formula.

Conic sections examples. Last saturday we were sitting around the house bored and watching tv. Hence all circles and all parabolas have the same shape only varying in size. For example all circles have zero eccentricity and all parabolas have unit eccentricity.

Conic sections can be generated by intersecting a plane with a cone. If α β the plane upon an intersection with cone forms a straight line containing a generator of the cone. General conic equation and eccentricity.

Conic sections are generated by the intersection of a plane with a cone. The conics curves include the ellipse parabola and hyperbola. Some real life examples of conic sections are the tycho brahe planetarium in copenhagen which reveals an ellipse in cross section and the fountains of the bellagio hotel in las vegas which comprise a parabolic chorus line according to jill britton a mathematics instructor at camosun college.

Introduction to conic sections by definition a conic section is a curve obtained by intersecting a cone with a plane. If α β 90 then the plane intersects the vertex exactly at a point. Conic sections examples if the plane intersects exactly at the vertex of the cone the following cases may arise.

Scroll down the page for more examples and solutions on conic sections. A cone has two identically shaped parts called nappes. One nappe is what most people mean by cone and has the shape of a party hat.

Eccentricity of conic sectionsthe eccentricity of a conic section completely characterizes its shape. Eccentricity of ellipse e c a a 2 b 2 a latus rectum of ellipse l b 2 a area of ellipse π a b.