Concept explainers
Sketch the ellipse using the latera recta
Answer to Problem 59E
The end points of the two latera recta are
Graph is shown below.
Explanation of Solution
Given:
To sketch the graph of the following ellipse using latera recta:
First find out the latera recta.
The Latus rectum is a line segment through a focus of an ellipse with end points on the ellipse and perpendicular to the major axis.
Thus, find the foci of the ellipse.
The standard equation of an ellipse with major axis vertical is
Comparing this with equation (1)
Thus, the center of the ellipse is
Also,
Next,
The foci li on the points
Thus, the foci are at
This tells that the two latera recta lie on the lines
To find out the intersection points of the two lines with the ellipse.
Substituting
Or
Thus, the end points of the two latera recta are
Thus, the graph of the ellipse can be drawn as below:
The two recta are depicted in the graph and their end-points marked.
Chapter 10 Solutions
EBK PRECALCULUS W/LIMITS
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning