GATE 2020 AE – Question 42

Engineering Mathematics · Calculus: Limits, continuity, differentiability, chain rule, maxima and minima, integration · 2 marks · Multiple choice

A closed curve is x = a cos θ, y = b sin θ, with a = 7 m and b = 5 m. Using π = 22/7, find its enclosed area.

110 m²
74 m²
35 m²
144 m²

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Correct answer: (A) 110 m²

Explanation

This parameterization describes an ellipse with semiaxes a,b. Area is $\pi ab=(22/7)(7)(5)=110$ m², A. The dimensions a and b are semiaxes, so an extra division by four is not appropriate.

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