Question

Consider the ellipse defined by the equation 공 = 1. What is the maximum area of a 81 9 rectangle inscribed in the ellipse? Enter only the maximum area and do not include any units.

Answer 1

To find the maximum area of a rectangle inscribed in an ellipse, substitute the dimensions of the rectangle in the ellipse equation, solve for a and b, and calculate the area of the rectangle using the length and width.

Step-by-step explanation:

To find the maximum area of a rectangle inscribed in an ellipse, we first need to determine the dimensions of the rectangle. Since the ellipse has the equation x²/a² + y²/b² = 1, we can substitute the dimensions of the rectangle, 81 and 9, to find the value of a and b. Solving 81/a² + 9/b² = 1 gives us the values of a and b. Once we have the values, we can calculate the area of the rectangle using the formula Area = length x width. Finally, we can determine the maximum area by evaluating all possible values of a and b.