Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question

Solve Conic equation

Here are two equations involving \( x \) and \( y \): 1. \[\frac{(x + 6)^2}{26} + \frac{y^2}{13} = 1\] This equation represents an ellipse. The center of this ellipse is shifted horizontally by -6 units (to the left) and the axes of the ellipse are scaled by the factors of \( \sqrt{26} \) and \( \sqrt{13} \). 2. \[x^2 + y^2 = 9\] This equation represents a circle with a radius of 3 units, centered at the origin (0,0). To explain what these equations represent graphically: - The first equation is an ellipse centered at (-6, 0) with axes lengths determined by \(\sqrt{26}\) along the x-axis and \(\sqrt{13}\) along the y-axis. - The second equation is a circle centered at the origin with a radius of 3 units. Together, these equations describe two different geometric shapes and their locations in a coordinate plane.
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Transcribed Image Text:Here are two equations involving \( x \) and \( y \): 1. \[\frac{(x + 6)^2}{26} + \frac{y^2}{13} = 1\] This equation represents an ellipse. The center of this ellipse is shifted horizontally by -6 units (to the left) and the axes of the ellipse are scaled by the factors of \( \sqrt{26} \) and \( \sqrt{13} \). 2. \[x^2 + y^2 = 9\] This equation represents a circle with a radius of 3 units, centered at the origin (0,0). To explain what these equations represent graphically: - The first equation is an ellipse centered at (-6, 0) with axes lengths determined by \(\sqrt{26}\) along the x-axis and \(\sqrt{13}\) along the y-axis. - The second equation is a circle centered at the origin with a radius of 3 units. Together, these equations describe two different geometric shapes and their locations in a coordinate plane.
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