Read the two statements and choose the correct option. I. The ellipse x^2/a^2 + y^2/b^2 = 1 encloses the same area as a circle of radius √(ab). II. The part of the ellipse x^2/a^2 + y^2/b^2 = 1 above the x-axis has area (π ab)/4.

Question 96

EasyOriginal question

Read the two statements and choose the correct option.
I. The ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ encloses the same area as a circle of radius $\sqrt{ab}$ .
II. The part of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ above the $x$ -axis has area $\frac{\pi ab}{4}$ .

Only ICorrect answerYour answerOnly IICorrect answerYour answerBoth I and IICorrect answerYour answerNeither I nor IICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

I: $\pi\left(\sqrt{ab}\right)^{2} = \pi ab$ , the area of the ellipse. True.
II: the part above the $x$ -axis is half the ellipse, $\frac{\pi ab}{2}$ ; $\frac{\pi ab}{4}$ is one quadrant. False.

Worth noting

Taking II as true confuses the half above the axis with the quarter in one quadrant.

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