# Parametric equation of the intersection between surfaces

 Math Emeritus Sci Advisor Thanks PF Gold P: 39,569 In a situation like that it is better not to solve for one of the variables. Instead, change x2+ y2= 1- y2 to x2+ 2y2= 1, the equation of an ellipse. Then use the "standard" parameterization of an ellipse: x= cos(t), y= sin(t)/$\sqrt{2}$. Then, of course, you can have either $z= cos^2(t)+ (1/2)sin^2(t)$ or $z= 1- (1/2)sin^2(t)$.