Multiple choice

The area of the rectangle of maximum area inscribed in the ellipse $\displaystyle \frac{{x}^{2}}{25}+\frac{{y}^{2}}{16}=1$ is

  1. $48$
  2. $41$
  3. $40$
  4. $50$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For an ellipse x^2/a^2 + y^2/b^2 = 1, the maximum area of an inscribed rectangle is 2ab. Here a=5, b=4. Area = 2 * 5 * 4 = 40.

AI explanation

The maximum area of a rectangle inscribed in an ellipse x^2/a^2 + y^2/b^2 = 1 is given by the product 2ab. From the given ellipse equation x^2/25 + y^2/16 = 1, we identify the semi-major axis as a = 5 and the semi-minor axis as b = 4. Calculating 2ab yields 2 * 5 * 4, which gives a maximum area of 40.

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