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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- Feb 7th 2009, 07:16 PMkrakraArea 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.. - Feb 7th 2009, 07:24 PMmr fantastic
Intersection of the two curves: Solve $\displaystyle x^2 + 2px = 4px$.

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 $\displaystyle x^2 + y^2 = 4px \Rightarrow (x - 2p)^2 + y^2 = 4 p^2$.

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.