Thread: ellipse

The figure at right shows one of the many rectangles that can be inscribed in the ellipse 4x2 + 9y2 = 36. The first-quadrant corner of this rectangle is (1.8, 1.6). Find the dimensions of the inscribed rectangle that has the largest area. It is not the one shown.

I am using quess and check now.
Is there a smarter approach?

Originally Posted by Veronica1999

The figure at right shows one of the many rectangles that can be inscribed in the ellipse 4x2 + 9y2 = 36. The first-quadrant corner of this rectangle is (1.8, 1.6). Find the dimensions of the inscribed rectangle that has the largest area. It is not the one shown.

I am using quess and check now.
Is there a smarter approach?

(a) start by solving the ellipse equation for y in terms of x.

(b) graph the equation A = xy (substituting what you got for y in part (a)) for the area of the rectangle in quad I.

(c) locate the maximum on the graph.