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^. Use linear algebra techniques to find the center and the radius of the circle a(x² + y²) + bx+cy + d = 0 through three given points (1,0), (-1, 2), and (3, 1). Sketch appropriate picture. Find all equations of circles a(x² + y²) + bx + cy + d = 0 through two given points (-1,2), and (3, 1). Sketch appropriate pictures.

^. Use linear algebra techniques to find the center and the radius of the circle a(x² + y²) + bx+cy + d = 0 through three given points (1,0), (-1, 2), and (3, 1). Sketch appropriate picture. Find all equations of circles a(x² + y²) + bx + cy + d = 0 through two given points (-1,2), and (3, 1). Sketch appropriate pictures.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Linear Algebra

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### Example Exercises on Circles #### A. Use linear algebra techniques to find the center and the radius of the circle \( a(x^2 + y^2) + bx + cy + d = 0 \) through three given points \((1, 0)\), \((-1, 2)\), and \((3, 1)\). Sketch appropriate picture. In this problem, you are to apply linear algebra concepts to determine the properties of a circle that passes through three specific points. Once you have the equation, identify the circle's center and its radius. Don't forget to sketch the circle as well as the points through which it passes for better visualization. #### B. Find all equations of circles \( a(x^2 + y^2) + bx + cy + d = 0 \) through two given points \((-1, 2)\), and \((3, 1)\). Sketch appropriate pictures. In this exercise, you need to find all possible circles that pass through two specific points. Write down the general equations for these circles and then represent them graphically. Sketching will help illustrate the various circles that meet the criteria of passing through the given points.
Transcribed Image Text:### Example Exercises on Circles #### A. Use linear algebra techniques to find the center and the radius of the circle \( a(x^2 + y^2) + bx + cy + d = 0 \) through three given points \((1, 0)\), \((-1, 2)\), and \((3, 1)\). Sketch appropriate picture. In this problem, you are to apply linear algebra concepts to determine the properties of a circle that passes through three specific points. Once you have the equation, identify the circle's center and its radius. Don't forget to sketch the circle as well as the points through which it passes for better visualization. #### B. Find all equations of circles \( a(x^2 + y^2) + bx + cy + d = 0 \) through two given points \((-1, 2)\), and \((3, 1)\). Sketch appropriate pictures. In this exercise, you need to find all possible circles that pass through two specific points. Write down the general equations for these circles and then represent them graphically. Sketching will help illustrate the various circles that meet the criteria of passing through the given points.
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