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Conic Sections Ellipse Part 3

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Additional Ellipse Elements Recall that the parabola had a directrix The ellipse has two directrices They are related to the eccentricity Distance from center to directrix =

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Directrices of An Ellipse An ellipse is the locus of points such that The ratio of the distance to the nearer focus to … The distance to the nearer directrix … Equals a constant that is less than one. This constant is the eccentricity.

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Directrices of An Ellipse Find the directrices of the ellipse defined by

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Additional Ellipse Elements The latus rectum is the distance across the ellipse at the focal point. There is one at each focus. They are shown in red

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Latus Rectum Consider the length of the latus rectum Use the equation for an ellipse and solve for the y value when x = c Then double that distance Length =

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Try It Out Given the ellipse What is the length of the latus rectum? What are the lines that are the directrices?

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Given equation of an ellipse We note that it is not a function Use this trick Graphing An Ellipse On the TI

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Set Zoom Square Note gaps due to resolution Graphing routine Specify an x Solve for zero of expression for y Graph the (x,y)

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Graphing Ellipse in Geogebra Enter ellipse as quadratic in x and y

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Area of an Ellipse What might be the area of an ellipse? If the area of a circle is …how might that relate to the area of the ellipse? An ellipse is just a unit circle that has been stretched by a factor A in the x-direction, and a factor B in the y-direction

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Area of an Ellipse Thus we could conclude that the area of an ellipse is Try it with Check with a definite integral (use your calculator … it’s messy)

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Assignment Ellipses C Exercises from handout 6.2 Exercises 69 – 74, 77 – 79 Also find areas of ellipse described in 73 and 79

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