P=(x, y)=(r· cos 4, r.sin 4) = dyldo dx/do %3D Formula: a%dx. dx/do %3D Sketch a the rectangular plot of the' Or - plane given equaon in the indicoted o interval. over Sketch polor graph of the where equation in the xyplane X =r cos o, rsin Find the slope and inclination of the tagent' ine to the polar curve at the point

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A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

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A: Solution of the problem as follows

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A: The parametrized curve x=e-sinθ and y=ecosθ for 0≤θ&lt;2π.

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A: We find the point of intersection by setting them equal

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A:

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A:

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A: we will use green theorem here to solve this question

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A:

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A:

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A: Explanation of the answer is as follows

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A: Follow 2nd and 3rd step.

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A: We have to point length of curve swept out by the point:

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A:

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A: Given:

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A: on solving this we get

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A: Given: To explain the correct of the given statement as follows,