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Area between ellipses
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Student 999
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#1
Looking through my working out I think could have elaborated a bit more on the last part of the question, how I got the expression of the area between E and F.
would something along the lines on how lines of symmetry exist of y=x and y=-x , hence in the first quadrant the upper enclosed area = the lower enclosed area .This applies to all 4 quadrants hence you multiply 8 by area of OCB.
I made a comment on how F is E rotated by 90 degrees, I could prove that via rotational matrices but the entire sentence itself doesn't really add value to my answer.![Name: Screenshot 2022-07-04 at 22.12.52.png
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would something along the lines on how lines of symmetry exist of y=x and y=-x , hence in the first quadrant the upper enclosed area = the lower enclosed area .This applies to all 4 quadrants hence you multiply 8 by area of OCB.
I made a comment on how F is E rotated by 90 degrees, I could prove that via rotational matrices but the entire sentence itself doesn't really add value to my answer.
Last edited by Student 999; 1 month ago
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Student 999
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#2
Just realised I could have saved a bit of time if I used part 2 and added to my integral in part 3 then multiplied by 4
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mqb2766
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#3
You may have (partially?) covered this with your second post, but the last part is simply
8 * (part ii - triangle)
so its just 8 times the second term from part ii. You shouldnt need to do any further integration here. Once youve noted the intersection point (c), you can just write the answer down.
Also, for parts i and ii), youve done them two seperate ways (both ok), but you could note that part ii) is a simple scaling in both the x and y axes of part i). Again, that would be simpler.
8 * (part ii - triangle)
so its just 8 times the second term from part ii. You shouldnt need to do any further integration here. Once youve noted the intersection point (c), you can just write the answer down.
Also, for parts i and ii), youve done them two seperate ways (both ok), but you could note that part ii) is a simple scaling in both the x and y axes of part i). Again, that would be simpler.
Last edited by mqb2766; 1 month ago
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