Presentation on theme: "Definition Equation Graph"— Presentation transcript:
1Definition Equation Graph WHAT IS AN ELLIPSE?DefinitionEquationGraph
2What is an ellipse?An ellipse is a conic section formed by the intersection of a plane and a cone.Click here to see an applet that will allow you to display and animate the intersection of a plane and the surface of a cone.
3DEFINITIONAn ellipse is the set of all points in the plane such that the sum of the distances from two fixed points (called foci) is constant.Note that this is clearly a geometrical definition and does not point out the relationship between an ellipse and its algebraic equation.
4EQUATIONAn ellipse with center at (x0 ,y0 ) can be defined algebraically in standard form by the equation:It is important to remember:a is the distance from the center to the end of major axisb is the distance from the center to the end of major axisc is the distance from the center to the focusa2 = b2 + c2
5GRAPHSWhen graphing an ellipse it is useful to remember these facts:center is (x0 ,y0 )length of the major axis is 2alength of the minor axis is 2bdistance between foci is 2aClick here to see how the equation for an ellipse relates to its graph.
6PRACTICELet’s try some practice problems and see what you have learned.Click here for more practice problems.Try these problems for more practice.
7WHY WOULD I WANT TO KNOW ABOUT ELLIPSES? Whispering GalleriesPlanetary OrbitsHaley’s CometLunar & Solar EclipsesElliptical Galaxies