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Obtain the differential equation of the family of plane curves described and sketch several representative members of the family. 1. Circles with center on the line y =-x and passing through the origin. Ans. (x^2-2xy-y^2) dx + (x^2+2xy-y^2)dy=0 2. Circles of radius unity. Use the fact that the radius of curvature is 1. Ans. (y")^2= [1 +(y')^2]^3

Obtain the differential equation of the family of plane curves described and sketch several representative members of the family. 1. Circles with center on the line y =-x and passing through the origin. Ans. (x^2-2xy-y^2) dx + (x^2+2xy-y^2)dy=0 2. Circles of radius unity. Use the fact that the radius of curvature is 1. Ans. (y")^2= [1 +(y')^2]^3

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 45E
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Obtain the differential equation of the family of plane curves described and sketch several representative members of the family. 1. Circles with center on the line y =-x and passing through the origin. Ans. (x^2-2xy-y^2) dx + (x^2+2xy-y^2)dy=0 2. Circles of radius unity. Use the fact that the radius of curvature is 1. Ans. (y")^2= [1 +(y')^2]^3
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