Thread: 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.

Originally Posted by kittycat

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, and

so,



if we can divide by it.

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.

Originally Posted by kittycat

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