I think this is what your instructor wants but I am not sure
16x^2+9y^2-8z=0
16x^2+9y^2=8z
16x^2/8z +9y^2/8z=1 an ellipse
x^2/[8z/16] + y^2/[8z/9]=1
{x/[8z/16]^1/2 }^2 +{y/[8z/9]^1/2}2=1
let a=8z/9
let b= 8z/16
there is an angle @ such that y/a=cos@ and y/a=sin@ so
[x,y]= [b cos@,a sin@]
as @ makes a complete revolution, the point [a sin@,b cos@] traverses the ellipse once.
[@ is the parameter that never appears on the curve]
as z changes the ellipse changes
Arthur
