1. ## cartesian plane

Let f(xy)=x+y . For a0 , the level set f(xy)=a is a closed curve in 2 . Find the area enclosed by this curve, as a function of a

2. Originally Posted by Sarah88
Let f(xy)=x+y . For a0 , the level set f(xy)=a is a closed curve in 2 . Find the area enclosed by this curve, as a function of a
Consider the rule for f(x, y) in each quadrant. Then you should see that f(x, y) = a defines a diamond with vertices at (a, 0), (0, a), (-a, 0) and (0, -a). It should be no trouble to get the area .....

3. Originally Posted by mr fantastic
Consider the rule for f(x, y) in each quadrant. Then you should see that f(x, y) = a defines a diamond with vertices at (a, 0), (0, a), (-a, 0) and (0, -a). It should be no trouble to get the area .....
|x| + |y| = a: By definition of the modulus operator:

x > 0 and y > 0: x + y = a.

x > 0 and y < 0: x - y = a.

x < 0 and y < 0: -x - y = a.

x < 0 and y > 0: -x + y = a.