# Thread: How to parametrize the edge of a circle?

1. ## How to parametrize the edge of a circle?

I need to figure out the max and min of the function f(x,y) = xy-ln(x^2+y^2) in the area 1/4 <= x^2 + y^2 <= 4.

Unless I'm mistaken this is a circle with an inner and an outer edge, so we should be able to use cos and sin for parametrization. I don't know how though. If it had been x^2 + y^2 <= 1, then we can set x=cos(t) and y=sin(t), but now that it's 1/4 and 4 I'm lost.

2. ## Re: How to parametrize the edge of a circle?

Originally Posted by Sabo
I need to figure out the max and min of the function f(x,y) = xy-ln(x^2+y^2) in the area 1/4 <= x^2 + y^2 <= 4.

Unless I'm mistaken this is a circle with an inner and an outer edge, so we should be able to use cos and sin for parametrization. I don't know how though. If it had been x^2 + y^2 <= 1, then we can set x=cos(t) and y=sin(t), but now that it's 1/4 and 4 I'm lost.
x = (1/4)cos(t); y = (1/4)sin(t) is a parametrization of the inner circle. Replace (1/4) with (4) for the outer.