Please talk about the method of solving the parametric equation by transforming triple integral, and the calculation method of curve and surface integral

Please talk about the method of solving the parametric equation by transforming triple integral, and the calculation method of curve and surface integral

The triple integral can be transformed into a parametric equation. We can find a t as an intermediate variable, so that the original independent variables X, y, Z become the functions of T, so that the original triple integral can be transformed into an integral about the variable t (if it is a definite integral, pay attention to the transformation of the upper and lower limits of the integral)

How does this parametric equation eliminate the parameter k
x=-k/(k^2+4)
y=4/(k^2+4)
The answer is 4x ^ 2 + y ^ 2-y = 0

Division of two formulas
x/y=-k/4
k=-4x/y
Substituting y = 4 / (k ^ 2 + 4)
So y = 4 / (16x ^ 2 / y ^ 2 + 4)
Simplify
4x^2+y^2-y=0