Area of the loop of the curve ay^2=x^2(a-x)

Question : Find Area of the loop of the curve ay^2=x^2(a-x)Solution: Given curve \[ay^2=x^2\left(a-x\right)\] (1) Substituting y=0 into above equation \[0=x^2\left(a-x\right)\] x=0, a From eqn (1) \[y=\pm\frac{x}{\sqrt a}\sqrt{x-a}\] So the area of the loop of the given curve \[A=2\int_{x=0}^{a}ydx\] \[=2\int_{x=0}^{a}{\frac{x}{\sqrt…

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