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Math Help - Area enclosed by two curves

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    Area enclosed by two curves

    Find area enclosed by the curves x^2+y^2=4px and y^2=2px

    I am not sure what to do with p..
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  2. #2
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    Quote Originally Posted by krakra View Post
    Find area enclosed by the curves x^2+y^2=4px and y^2=2px

    I am not sure what to do with p..
    Intersection of the two curves: Solve x^2 + 2px = 4px.

    Draw a sketch of each curve for the cases p > 0 and p < 0 and shade the required area. By symmetry the required area is the same for both cases so you only have to find it for one of these cases.

    Note that x^2 + y^2 = 4px \Rightarrow (x - 2p)^2 + y^2 = 4 p^2.

    Now set up the required integral and solve it.

    If you're still struggling, start by giving p a concrete value like p = 1 to get the feel of things.
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