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Math Help - cartesian plane

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    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
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    Quote Originally Posted by Sarah88 View Post
    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 .....
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    Quote Originally Posted by mr fantastic View Post
    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.
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