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Math Help - Converting Cones in Spherical Polar Coor to Cartesean.

  1. #1
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    Converting Cones in Spherical Polar Coor to Cartesean.

    Find an equation in rectangular coordinates of the quadric surface consisting of the following two cones.


    I havent a CLUE how to start this
    please help

    i was thinking of converting the cones via the normal conversion methods, but then i lost myself

    ive never dealt with conical surfaces in any spaces...
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  2. #2
    MHF Contributor Calculus26's Avatar
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    z= pcos(phi)

    z= sqrt(x^2+y^2+z^2)cos(phi)

    z^2 = (x^2 +y^2 +z^2)cos^2(pi/6)

    z^2 = 3/4(x^2 +y^2 +z^2)

    z^2/4 = 3/4(x^2 +y^2)

    z^2 = 3(x^2 +y^2)

    z = sqrt(3)sqrt(x^2 + y^2)
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  3. #3
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    your the man
    thanks dude
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  4. #4
    MHF Contributor Calculus26's Avatar
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    Note fro phi = 5pi/6 the cone is in the bottom four octants

    The calculation is the same but take the negative sqrt of z

    z = - sqrt(3)sqrt(x^2 + y^2)
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  5. #5
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    that worked well enough
    i should of seen that but oh well

    thanks again
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