# Explicit Solution to Euler Lagrange Equation of Shortest Distance between two Points

So if $$f(t)=(x(t),y(t))$$ with $$f(0)=a$$ and $$f(1)=b$$, I should minimize $$L(f)=\int_0^1{|\dot{f(t)}|}dt$$. I get a jumble of equations when solving the Euler Lagrange equations with respect to $$t$$. Would someone help explicitly solving them. Please avoid using $$y'(x)$$ since I am trying to generalize this to n space

Thanks in advanced for any help.

Hint: Consider the squared Lagrangian cf. e.g. this Math.SE post. The shortest curve between $$a$$ and $$b$$ is unsurprisingly a straight line.