Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa58f16bd-f2f3-4ae0-8921-3cebc7a5838f%2F7da4a86d-7651-4f56-962b-2febda4d1733%2Fed5znq7_processed.jpeg&w=3840&q=75)
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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