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Area of Bounded Regions · Question 102 of 115

What is the area of the region inside the ellipse but outside Q?

Question 102

MediumOriginal question

The ellipse x236+y216=1\frac{x^{2}}{36} + \frac{y^{2}}{16} = 1 meets the axes at (±6,0)(\pm 6, 0) and (0,±4)(0, \pm 4). Joining these four points in turn gives a quadrilateral QQ inside the ellipse.

What is the area of the region inside the ellipse but outside QQ?

Options for question 102

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. Inside the ellipse and outside QQ is the ellipse with QQ taken away.

  2. 24π−4824\pi - 48 square units: four equal pieces of 6π−126\pi - 12, one between each quarter of the ellipse and its chord.

Worth noting

6π−126\pi - 12 is the piece in one quadrant; there are four.

Concept
A part from the whole
Typical time
120 s
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