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Equation of a sphere

  1. Aug 18, 2016 #1
    • Member warned about posting without the HW template
    I have been given a problem with 4 equations, that need to be matched up to the corresponding image. I have worked the equations already and determined their center, but for the life of me I cannot seem to figure out which graph goes with which equation. The images are not that easy to read which is most of my issue. Here is an example:

    x2−4x+y2−4y+z2−2z = -35/4 (original equation)

    (x-2)^2 + (y-2)^2 + (z-1)^2 -9 = -35/4

    (x-2)^2 + (y-2)^2 + (z-1)^2 = -35/4 + 9 >> √1/4 >> 1/2
    C = (2,2,1) r = 1/2


    This would give me a center of (2,2,1). However, none of the spheres I am provided appear to match this. Am I blind or does my math appear to be off? spheres.PNG
     
    Last edited: Aug 18, 2016
  2. jcsd
  3. Aug 18, 2016 #2

    mfb

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    (D) could fit. There are sign errors in your absolute values (doesn't influence the center, but influences the radius) - with your current number you would not get a sphere because the equation has no solution.
     
  4. Aug 18, 2016 #3
    I see that, I have it written down correctly on my notebook, resulting in a r of 1/2. I appreciate your response, at this point I am more concerned with getting the correct values than matching to the correct graph. There are 4 total equations, and if even one of the choices are wrong it marks the entire problem wrong. Prevents guessing I suppose, but not very helpful otherwise.
     
  5. Aug 18, 2016 #4

    Ray Vickson

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    ##x^2 - 4x = x^2 - 4x + 4 - 4 = (x-2)^2 -4##, etc. So, you should have ##-9## as the constant on the left of your final equation, not the ##+9## that you wrote. I cannot see what work you did to get your solution, so I don't know what steps you took.
     
  6. Aug 18, 2016 #5
    My apologies for the typo, I corrected it in the original post. Ultimately, I have what I believe is the correct values, but I am not seeing a sphere whose center is (2,2,1) with a radius of 1/2. The attachment is the image with the spheres, I'm not sure if it shows up embedded in the first post or not.
     
  7. Aug 18, 2016 #6

    Ray Vickson

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    I cannot see any sphere with center (2,2,1), or even close to it. Are you sure you copied down the original problem correctly?
     
  8. Aug 18, 2016 #7
    This is the original problem, directly from my assignment. #1 is the one in question. I will say that I failed to use "^" on the 3 variables to plainly indicate that they are squared, but I treated them as such and completed the squares.
    upload_2016-8-18_13-8-59.png
    Just in case the attachment doesnt work, x^2 - 4x +y^2 - 4y +z^2 - 2z = -35/4
     
  9. Aug 18, 2016 #8

    Ray Vickson

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    One of these equations fits one of the diagrams perfectly (as far as my eyes can make out). I can't say more without giving a way the solution.
     
  10. Aug 18, 2016 #9
    I agree, I have worked out the other 3 equations and was able to match 2 of them with a diagram fairly easily. But I still have to figure out which one matches the 1st equation(all 4 equations are supposed to be represented in the diagram). Are you saying you do see one with (2,2,1)? If so that's good enough for me, and I will keep staring until I see it, haha. In any case I appreciate the help.
     
  11. Aug 18, 2016 #10

    mfb

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    I see a sphere where (2,2,1) as center would fit. You cannot extract the coordinates from the images reliably (2 vs. 3 dimensions), but you can go the opposite way: see where (2,2,1) is in each image, and see if that matches the center of the sphere in the plane.
     
  12. Aug 18, 2016 #11

    Ray Vickson

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    As I said, I don't see any sphere with center near (2,2,1), but, apparently, others can.
     
  13. Aug 18, 2016 #12

    SammyS

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    Neither can I see any sphere with center near (2,2,1) .
     
  14. Aug 18, 2016 #13

    mfb

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    Do we see the same image?

    sphere.png
     
  15. Aug 18, 2016 #14

    Ray Vickson

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    To me it looks like the center is at about (0,1.5,0). However, as you said before, some of the figures are not very clear.
     
  16. Aug 18, 2016 #15
    One thing is certain, this problem is more of a test of your visual skills rather than testing your ability to solve an equation.. I have reached out to my TA to see if there is any help they can provide as well. I appreciate the help everyone
     
  17. Aug 18, 2016 #16

    mfb

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    You cannot uniquely determine the center of a 3D point from a 2D drawing without any additional help. The sphere in D is at the place where a sphere around (2,2,1) has to appear, and no other sphere fits.
     
  18. Aug 18, 2016 #17

    Ray Vickson

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    Assuming, of course, that the person setting the problem has not given an erroneous statement.
     
  19. Aug 18, 2016 #18

    mfb

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    Why?
    Sorry, I don't understand the problem. We are supposed to find the right sphere for this equation, there is exactly one sphere that fits. What needs further discussion?
     
  20. Aug 18, 2016 #19

    Ray Vickson

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    Whether it is correct that every one of the equations will, in fact, fit one of the displayed spheres. In other words, is the wording of the problem accurate?

    Sometimes problem statements given in this Forum have turned out to be wrong, more often than not because of typos, or whatever. Certainly, typos are not so rare as to be dismissable right away.
     
  21. Aug 18, 2016 #20

    mfb

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    Just one of the four equations has been posted here, but this one fits to exactly one sphere.

    If the problem statement doesn't seem to be right: sure. But here there is no problem with the problem statement. If you have to pick the answer to "5+5" and the options are "9", "10" and "15", you wouldn't expect a problem with the problem statement, right?
     
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