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Area of Bounded Regions · Question 107 of 115

Match each ellipse in List I with the area it encloses in List II.

Question 107

MediumOriginal question

Match each ellipse in List I with the area it encloses in List II.

List IList II
A. x29+y2=1\frac{x^{2}}{9} + y^{2} = 1I. 2π2\pi
B. 4x2+y2=44x^{2} + y^{2} = 4II. 12π12\pi
C. x2+4y2=36x^{2} + 4y^{2} = 36III. 3π3\pi
D. 9x2+16y2=1449x^{2} + 16y^{2} = 144IV. 18π18\pi
Options for question 107

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. A: a=3a = 3, b=1b = 1. B: dividing by 4, x2+y24=1x^{2} + \frac{y^{2}}{4} = 1, so a=1a = 1, b=2b = 2.

  2. C: x236+y29=1\frac{x^{2}}{36} + \frac{y^{2}}{9} = 1, area π×6×3\pi \times 6 \times 3. D: x216+y29=1\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1, area π×4×3\pi \times 4 \times 3.

Worth noting

Swapping A and B misreads B: dividing 4x2+y2=44x^{2} + y^{2} = 4 by 4 gives the semi-axes 1 and 2.

Concept
Area of a region of an ellipse
Typical time
120 s
Your time
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The rule this testsEllipses
Practise this chapter →

Ten questions from Area of Bounded Regions, at your own pace.

Practise this chapter →

Ten questions from Area of Bounded Regions, at your own pace.