Question

What is the area of the largest rectangle that can be inscribed in an ellipse? The maximum area is achieved when the rectangle's ___________.

A. Length equals the ellipse's major axis
B. Width equals the ellipse's minor axis
C. Length and width are equal
D. Length and width are at a 45-degree angle

Answer 1

The area of the largest rectangle that can be inscribed in an ellipse is achieved when the rectangle's length equals the ellipse's major axis.

Step-by-step explanation:

The area of the largest rectangle that can be inscribed in an ellipse is achieved when the rectangle's length equals the ellipse's major axis. This means that option A is correct.

To understand why, imagine an ellipse with its major axis along the x-axis and its minor axis along the y-axis. The length of the rectangle needs to be equal to the major axis, as it spans from one end of the ellipse to the other. Meanwhile, the width of the rectangle can be any value as long as it fits inside the ellipse. Therefore, the maximum area is achieved when the rectangle's length equals the ellipse's major axis.