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The standard equation of an ellipse with vertices at (-8, 0) and (8, 0) and minor axis 10 units is: OA. x2 y² 100 64 OB. x2 8 + OC. x² + 64 OD. x² v2 y 8 32 + = 1 25 5 + = 1 1 y² 10 = 1

The standard equation of an ellipse with vertices at (-8, 0) and (8, 0) and minor axis 10 units is: OA. x2 y² 100 64 OB. x2 8 + OC. x² + 64 OD. x² v2 y 8 32 + = 1 25 5 + = 1 1 y² 10 = 1

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Question 11** The standard equation of an ellipse with vertices at \((-8, 0)\) and \((8, 0)\) and minor axis 10 units is: A. \(\frac{x^2}{64} + \frac{y^2}{100} = 1\) B. \(\frac{x^2}{8} + \frac{y^2}{5} = 1\) C. \(\frac{x^2}{64} + \frac{y^2}{25} = 1\) D. \(\frac{x^2}{8} + \frac{y^2}{10} = 1\) *Explanation for Students:* An ellipse with vertices at \((-8, 0)\) and \((8, 0)\) is centered at the origin \((0, 0)\) and has a horizontal major axis. The distance between the vertices, 16 units, represents the length of the major axis, so \(a = 8\) since \(2a = 16\). The minor axis is 10 units long, so \(b = 5\) since \(2b = 10\). The correct equation follows the formula for the standard form of an ellipse: \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\).
Transcribed Image Text:**Question 11** The standard equation of an ellipse with vertices at \((-8, 0)\) and \((8, 0)\) and minor axis 10 units is: A. \(\frac{x^2}{64} + \frac{y^2}{100} = 1\) B. \(\frac{x^2}{8} + \frac{y^2}{5} = 1\) C. \(\frac{x^2}{64} + \frac{y^2}{25} = 1\) D. \(\frac{x^2}{8} + \frac{y^2}{10} = 1\) *Explanation for Students:* An ellipse with vertices at \((-8, 0)\) and \((8, 0)\) is centered at the origin \((0, 0)\) and has a horizontal major axis. The distance between the vertices, 16 units, represents the length of the major axis, so \(a = 8\) since \(2a = 16\). The minor axis is 10 units long, so \(b = 5\) since \(2b = 10\). The correct equation follows the formula for the standard form of an ellipse: \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\).
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