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Theory and ExamplesThe family of straight lines y = ax + b
Chapter 4, Problem 24AAE(choose chapter or problem)
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.)
Questions & Answers
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