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

Equation of the sufboard:
x^2/16+y^2=1 

Looks pretty good to me!