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Equation of curves (intersection)

  1. Apr 24, 2010 #1
    1. The problem statement, all variables and given/known data

    Let [itex] S [/itex] be the solid region bounded by the paraboloid [itex] z = x^2 + y^2 - 4 [/itex] for [itex] z \le 0 [/itex], [itex] 0 \le x \le \sqrt{4 - y^2} [/itex] and [itex] 0 \le y \le 2 [/itex]. Find the Cartesian equations of the curves if the surface S intersects the [itex] xy,xz [/itex], and [itex] yz [/itex] planes.

    3. The attempt at a solution

    Is the question asking us to find the equation of the intersection of [itex] z = x^2 + y^2 - 4 [/itex] and [itex]z=z[/itex], [itex]z=x[/itex], and [itex]z=y[/itex] respectively?

    As I am confused with this question and not really sure how to start, so there is no attempt yet but I had some thought about this question. Could you tell me some hints to start the problem?

    Last edited: Apr 24, 2010
  2. jcsd
  3. Apr 24, 2010 #2


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    i would take the xy plane to be where z = 0
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