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Math Help - define Region R limits =urgent please

  1. #1
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    Question define Region R limits =urgent please

    given :
    region R is x^2+y^2=2ax

    we need to define the limit of R in terms of (r, theta) .

    I got the answer from the book is 0< or = r < or = 2acostheta. I don't understand how this limit from. Could you please explain to me? Thank you very much.

    For the theta limit is from -pi/2 to pi/2 . That is okay. I got this part.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by kittycat View Post
    given :
    region R is x^2+y^2=2ax

    we need to define the limit of R in terms of (r, theta) .

    I got the answer from the book is 0< or = r < or = 2acostheta. I don't understand how this limit from. Could you please explain to me? Thank you very much.

    For the theta limit is from -pi/2 to pi/2 . That is okay. I got this part.
    no big deal here, they just switched to polar coordinates

    recall that in polar coordinates, x^2 + y^2 = r^2 and x = r \cos \theta

    so, x^2 + y^2 = 2ax

    \Rightarrow r^2 = 2a r \cos \theta

    if r \ne 0 we can divide by it.

    \Rightarrow r = 2a \cos \theta
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    Hi Jhevon,
    x^2 + y^2 = 2ax
    then (x-a)^2 + y^2 = a^2

    so we notice that this is a circle of radius a centered at (a, 0).

    why can't we say that r's limits is from 0 < or = r < or = 2a?

    Please teach me . thank you very much.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by kittycat View Post
    Hi Jhevon,
    x^2 + y^2 = 2ax
    then (x-a)^2 + y^2 = a^2

    so we notice that this is a circle of radius a centered at (a, 0).

    why can't we say that r's limits is from 0 < or = r < or = 2a?

    Please teach me . thank you very much.
    because, we measure r from (0,0) not (a,0). we have to account for the circle's center shifting from the origin, we do that as i did above
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