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Thomas' Calculus: Early Transcendentals | 13th Edition | ISBN: 9780321884077 | Authors: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass
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Theory and ExamplesThe family of straight lines y = ax + b

Chapter 4, Problem 24AAE

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QUESTION:

Problem 24AAE

Theory and Examples

The family of straight lines y = ax + b (a, b arbitrary constants) can be characterized by the relation Find a similar relation satisfied by the family of all circles  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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QUESTION:

Problem 24AAE

Theory and Examples

The family of straight lines y = ax + b (a, b arbitrary constants) can be characterized by the relation Find a similar relation satisfied by the family of all circles  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.)

ANSWER:

Solution

Step 1 of 3

In this problem we need to determine the differential equation of family of circles.

Given equation

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