In sensitivity analysis one wants to know how the problem and the optimal solutions change under the variation of the input data. We consider the case when variation happens in the right-hand side of the constraints and/or in the linear term of the objective function. We are interested to find the range of the parameter variation in Convex Quadratic Optimization (CQO) problems where the support set of a given primal optimal solution remains invariant. This question has been first raised in Linear Optimization (LO) and known as Type II (so-called Support Set Invariancy) sensitivity analysis. We present computable auxiliary problems to identify the range of parameter variation in support set invariancy sensitivity analysis for CQO. It should be mentioned that all the given auxiliary problems are LO problems and can be solved by an interior point method in polynomial time. We also highlight the differences between the characteristics of support set invariancy sensitivity analysis for LO and CQO.