The rectangular wooden piece will have area as: [tex]\dfrac{x^2}{900} +\dfrac{y^2}{400}=1[/tex]
An ellipse can be defined as a shape that looks like an oval circle.
For this case, as we have a rectangular piece of board the maximum ellipse will have a major axis of the length of 60 inches, and a minor axis of 40 inches.
Thus, we have:
a= 60/2 = 30 inches
b= 40/2 = 20 inches
Thus, if the rectangle is placed such that the major axis is on the x-axis, and the minor axis is on the y-axis, then the equation of that ellipse would be:
[tex]\dfrac{x^2}{30^2} +\dfrac{y^2}{20^2}=1[/tex]
[tex]\dfrac{x^2}{900} +\dfrac{y^2}{400}=1[/tex]
Thus, the largest ellipse that the artist can make on the considered rectangular wooden piece will have the area as: [tex]\dfrac{x^2}{900} +\dfrac{y^2}{400}=1[/tex]
(assuming its major and minor axes lie onthe x and y axis respectively)
Learn more about ellipse here:
https://brainly.com/question/9448628
#SPJ5
