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12. What's the solution set to the following system? x² + y² = 9 9x² +25y² = 225

12. What's the solution set to the following system? x² + y² = 9 9x² +25y² = 225

Calculus: Early Transcendentals
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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## Problem 12: Solving the System of Equations **Question:** What's the solution set to the following system of equations? **Equations:** 1. \( x^2 + y^2 = 9 \) 2. \( 9x^2 + 25y^2 = 225 \) **Options:** - **A.** \(\{(3, 0), (-3, 0)\}\) - **B.** \(\{(0, 5), (0, -5)\}\) - **C.** \(\{(5, 0), (-5, 0)\}\) - **D.** \(\{(0, 3), (0, -3)\}\) **Explanation:** The first equation, \( x^2 + y^2 = 9 \), represents a circle centered at the origin with a radius of 3. The second equation, \( 9x^2 + 25y^2 = 225 \), can be rewritten as the ellipse \(\left(\frac{x^2}{25}\right) + \left(\frac{y^2}{9}\right) = 1\), which is an ellipse centered at the origin, with semi-major axis 5 and semi-minor axis 3. To find the solution set, determine the points that satisfy both equations simultaneously.
Transcribed Image Text:## Problem 12: Solving the System of Equations **Question:** What's the solution set to the following system of equations? **Equations:** 1. \( x^2 + y^2 = 9 \) 2. \( 9x^2 + 25y^2 = 225 \) **Options:** - **A.** \(\{(3, 0), (-3, 0)\}\) - **B.** \(\{(0, 5), (0, -5)\}\) - **C.** \(\{(5, 0), (-5, 0)\}\) - **D.** \(\{(0, 3), (0, -3)\}\) **Explanation:** The first equation, \( x^2 + y^2 = 9 \), represents a circle centered at the origin with a radius of 3. The second equation, \( 9x^2 + 25y^2 = 225 \), can be rewritten as the ellipse \(\left(\frac{x^2}{25}\right) + \left(\frac{y^2}{9}\right) = 1\), which is an ellipse centered at the origin, with semi-major axis 5 and semi-minor axis 3. To find the solution set, determine the points that satisfy both equations simultaneously.
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