Two promotional stands are to be placed in an ellipse-shaped room—one at each foci—and are 3 units from the center. if the room is 8 units wide, what is its length?

We are given the value of a and c; a is the width of the ellipse and c is the focus of the ellipse. For an ellipse the equation to be used to find b or the length of the ellipse is:

a^2 = b^2 + c^2

substitute the values in the equation to solve for the missing variable:

8 units is 2a, therefore, a = 4

4^2 = b^2 + 3^2

solve for b:

b = √7 units

Therefore, the value of b is √7 units. To solve for the length of the ellipse (2b), multiply b with 2:

2b = √7 * 2
Length = 2√7 units