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Circle equation help

  1. May 14, 2005 #1
    hi, I am stuck on this question for homework :

    I'm not sure how to find the answer, as I thought integration is used only if the curve intersects at the x axis ? :confused:


    Thanx for any help


    1.) The equation of circle x^-8x+y^2-10y=-16

    It intersects the y axis at two points : (0,2) and (0,8)

    Find the small area between the curve and the y axis.(on the left of the y axis)


    2.) Also, the chord between 0,2 and 0,8 on the circle subtends an angle at the centre (4,5).

    Show that the angle is 7/25 using the cosine rule.


    I'm not sure what to do here as well..
     
  2. jcsd
  3. May 14, 2005 #2

    dextercioby

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    Plot that circle and then decide whether u'll be needing calculus to find that area.

    As for the second,i don't follow.Is it the same circle...?

    Daniel.
     
  4. May 14, 2005 #3

    The area is bound between the y axis and the circle. But I don't see how else it could be done without calculus ?

    The second question is the same circle and I need to find the angle .
    (0,2) and (0,8) is the chord on the circle .
     
  5. May 14, 2005 #4

    dextercioby

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    Alright,then,write the equation and see which branch of the explicitation will u be needing (hint:u can explicitate "x" as a function of "y",because you're given the intercepts with the Oy axis).

    Daniel.
     
  6. May 14, 2005 #5

    I've not heard that word before...explicitate ..

    but I dont understand what your saying.
     
  7. May 14, 2005 #6

    dextercioby

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    Hmmm,alright.Your equation's typically

    [tex] (x-x_{0})^{2}+(y-y_{0})^{2}=1 [/tex]

    Express x=x(y).

    Daniel.
     
  8. May 14, 2005 #7

    I dont get it :grumpy:


    especially
    Express x=x(y).
     
  9. May 14, 2005 #8

    dextercioby

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    You need to put somethting,a function,in this integral

    [tex] \mbox{Area}=\int_{\mbox{intercept no.1}}^{\mbox{intercept no.2}} f(y) \ dy [/tex]

    And that function of "y" (f(y)) is the one u'll be getting from the circle's equation.

    Daniel.
     
  10. May 14, 2005 #9

    okay, and then take away the the intercept 2 - 1 ?

    but what does x(y)=x mean ? I need a thorough explanation on this please.
     
  11. May 14, 2005 #10

    dextercioby

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    It's a notation;x=x(y) means the function "x" written in terms of the variable "y".

    Daniel.
     
  12. May 14, 2005 #11

    but if i took away the 1st from the second integral is the order important ?

    what difference does it make ?

    If the area was not bound by either x or y axis is there a direct way to calulate the area?
     
  13. May 14, 2005 #12

    dextercioby

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    Yes,of course.The area of a plane domain [itex] D\subseteq\mathbb{R}^{2} [/itex] is given by

    [tex] S_{D}=:\iint_{D} dx \ dy [/tex]

    as long as u choose Oxy as a set of orthormal coordinates in the plane.

    Daniel.
     
  14. May 15, 2005 #13

    Daniel, what difference would it make if I wrote g(y)=x ?
     
  15. May 15, 2005 #14

    arildno

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    The difference is that x=x(y) is a "loose/sloppy" notation, whereas x=g(y) is an example of a "rigorous/careful" notation. That's basically it.
     
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