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  • Apr 8, 2009, 04:32 PM
    Music4Life
    calc II homework
    Consider the parabola given by the equation y^2-2x-6y+11=0
    How to get it in Standard Form and find the vertex and focus
  • Apr 8, 2009, 04:37 PM
    Music4Life
    Math Homework: Calc II
    Find the center of the ellipse
    5x^2+2y^2-20x+24y+82=0
  • Apr 8, 2009, 04:41 PM
    Music4Life
    Math Homework:Calc II
    Find the length of the curve over the given interval
    r=8(1+cos(angle), 0<angle<2(3.124)
  • Apr 8, 2009, 04:46 PM
    Music4Life
    Math Homework: Calc II
    Find the area of the region.
    interior of r=5(1+sin(angle))

    and

    One petal of r=cos(5(angle))
  • Apr 8, 2009, 06:48 PM
    galactus
    2 Attachment(s)
    Quote:

    Originally Posted by Music4Life View Post
    Find the area of the region.
    interior of

    and

    One petal of

    Is this one problem or two? I am going to treat it as two different regions.





    Now, integrate away.

    As for the rose, to find the limits of integration, solve

    We find

    Multiply by 2 because of symmetry.

  • Apr 8, 2009, 06:56 PM
    galactus
    Quote:

    Find the length of the curve over the given interval





    Polar arc length is given by:





    I assume you are integrating from 0 to





    This integral can be a little tricky. As a matter of fact, most calculators grunt trying to do it, but it ain't that bad if we use some tricks.











    Now, let

    We end up with something easy:



    Resub:



    Let's integrate from 0 to Pi and multiply by 2 because using 2Pi presents a conundrum. Do you see why?



    There it is.
  • Apr 8, 2009, 07:01 PM
    galactus
    Quote:

    Find the center of the ellipse




    Complete the square.







    Now, can you finish and get into the form of an ellipse? Just one more step.

    Though, you can easily see the center coordinates as it is now.
  • Apr 8, 2009, 07:05 PM
    galactus
    Quote:

    Consider the parabola given by the equation
    How to get it in Standard Form and find the vertex and focus


    As with the ellipse, complete the square.

    The standard form of this parabola is , where (h,k) are the vertex coordinates.

    It is a parabola opening to the right symmetric about y=3. The directrix is at x=1/2.









    The focus can be found by using .

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