A latus rectum for an ellipse is a line segment perpendicular to the major axis at a focus, with endpoints on the ellipse, as shown in the figure. y Latus rectum -a Foci Show that the length of a latus rectum is 262/a for the ellipse a> b. The foci of the given ellipse are (?v, 0), where c = a - b. If the endpoints of one latus rectum are the points (c, tk), then the length of one latus rectum is Substitute one of the endpoints into the given equation for the ellipse and solve for k. a2 22 k2 = Substitute b2 for 32 - 2. 22 k = Thus, the length of a latus rectum for the given ellipse is 2k =

A latus rectum for an ellipse is a line segment perpendicular to the major axis at a focus, with endpoints on the ellipse, as shown in the figure. y Latus rectum -a Foci Show that the length of a latus rectum is 262/a for the ellipse a> b. The foci of the given ellipse are (?v, 0), where c = a - b. If the endpoints of one latus rectum are the points (c, tk), then the length of one latus rectum is Substitute one of the endpoints into the given equation for the ellipse and solve for k. a2 22 k2 = Substitute b2 for 32 - 2. 22 k = Thus, the length of a latus rectum for the given ellipse is 2k =

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter12: Conic Sections

Section12.2: Ellipses

Problem 64E: How Wide Is an Ellipse at a Focus? A latus rectum for an ellipse is a line segment perpendicular to...

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How Wide Is an Ellipse at a Focus? A latus rectum for an ellipse is a line segment perpendicular to the major axis at a focus, with endpoints on the ellipse, as shown in the figure. Show that the length of a latus rectum is 2b2/a for the ellipse x2a2+y2b2=1a>b
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