surfboard company would like to design a new long board in the shape of an ellipse. The surfboard should be 8 feet long and 2 feet wide. Find the equation of the surfboard. Assume that the center is located at 0,0, that the surfboard is lying on the ground horizontally, and that one foot is equivalent to one coordinate unit.

Length: L=8 feet

Width: W=2 feet

Center is located at 0,0 → C = (0,0) = (h, k) →h=0, k=0

The surfboard is lying on the ground horizontally:

x^2/a^2+y^2/b^2=1

L=2a→2a=8 feet

Solving for a:

2a/2 = (8 feet) / 2

a=4 feet

W=2b→2b=2 feet

Solving for b:

2b/2 = (2 feet) / 2

b=1 feet

Replacing a=4 and b=1 in the equation (1):

(1) x^2/a^2+y^2/b^2=1

x^2/4^2+y^2/1^2=1

x^2/16+y^2/1=1

x^2/16+y^2=1

Answer: Equation of the sufboard:

x^2/16+y^2=1