Yoga requires commitment: commitment to showing up on a regular basis, to being willing to gently try even when you feel tired or checked out, to being open to whatever presents itself, to responding to what is actually happening and not to what you think should be happening. As I'm sure you've heard many times and in many forms, yoga is about being true to the present moment. This means developing our conscious ability to observe and participate, and learning how to use our asana practice as a forum for experiencing and enhancing this awareness.
Being present, however, also means that we cannot come onto our yoga mat with an agenda. Often when we "make a determination" or are "determined," we become committed to a plan or an idea that obstructs our ability to be open to the present moment. Therefore, instead of approaching your asana with "determination," think of approaching your practice with equal parts patience and persistence. This way you still have committed energy, but in a somewhat less rigid form.