Which of the following statements are true? I. The area of the ellipse x^2/a^2 + y^2/b^2 = 1 is π ab. II. An ellipse with a = b is a circle, and π ab becomes π a^2. III. The area of x^2/a^2 + y^2/b^2 = 1 is π(a + b). IV. Doubling both semi-axes of an ellipse multiplies its area by 4.

Question 98

MediumOriginal question

Which of the following statements are true?
I. The area of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ is $\pi ab$ .
II. An ellipse with $a = b$ is a circle, and $\pi ab$ becomes $\pi a^{2}$ .
III. The area of $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ is $\pi(a + b)$ .
IV. Doubling both semi-axes of an ellipse multiplies its area by 4.

I and II onlyCorrect answerYour answerAll four: I, II, III and IVCorrect answerYour answerII and IV onlyCorrect answerYour answerI, II and IV onlyCorrect answerYour answer

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CorrectNot quiteAnswer D

Correct answer: D

I, II and IV hold: $\pi(2a)(2b) = 4\pi ab$ .
III is false: $\pi(a + b)$ is not even in square units of length times length.

Concept: The area of an ellipse
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsEllipses

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