The family of straight lines y = ax + b (a, b arbitrary constants) can be characterized by the relation y′′ = 0. Find a similar relation satisfied by the family of all circles (x - h)2 + (y - h)2 = r2, where h and r are arbitrary constants. (Hint: Eliminate h and r from the set of three equations including the given one and two obtained by successive differentiation.)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
Question

The family of straight lines y = ax + b (a, b arbitrary constants) can be characterized by the relation y′′ = 0. Find a similar relation satisfied by the family of all circles (x - h)2 + (y - h)2 = r2, where h and r are arbitrary constants. (Hint: Eliminate h and r from the set of three equations including the given one and two obtained by successive differentiation.)

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