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Homework Statement
Homework Equations
The Attempt at a Solution
This problem belongs to the topic "calculus of variation ". The fundamental problem of “calculus of variation” is to find a function y(x) such that the integral ## I = \int_{x_i }^{ x_f} \phi (y’, y, x) ~d x ## is extremum, where ## \phi (y', y, x) ## is a functional. Then, I have to use Euler  Lagrange Equation to find out y(x).
Here, I am not able to formulate the problem using the calculus of variation technique.
Another approach is to find out the function expressing the circle in ## \phi ##  plane, i.e. f( ##\phi ## , y,x) and then use df = 0 to find out the points of maximum and minimum. Then I don’t know how to find out the function f?
Is this correct till now?
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