Help solve a minimization problem using geometry only

[claudiocamera]

Given the minimization problem

min x²+y²
Subjec to 2x+y = c where c is a constant.
How to find grafficaly(geometricaly) the minimum point.
Applying the optimization theorems using gradient and hessian will we find x=2c/5 and y = c/5. But how to get such result only using geometry?

 

[wave-maniac]

Minimization problem

Dear claudiocamera,
I hope I'm not missing anything. The solution seems to be as follows:
Draw the line 2X+Y=C then draw a line from (0,0) perpendicular to it. The intersection point will be the optimum point. The minimum value will be the second line length squared.