Stub matching and SWR circle

I am familiar with T lines but not so much with smith chart. so trying to fix that now. I am trying to match a load to the Zo.

After plotting ZL on the smith chart, why is it important to move along the constant SWR circle until it intersects the rotated 1 + jx circle or the 1 + jb circle (assuming ZL is outside the 1+ jx circle)

the actual location of the impedance does not matter in my question - but why move along the SWR circle - to maintain the same reflection coefficient ?

there arent any books or links that intuitively explains this to me about stubs. this is a difference when compared to LC matching networks where we move along constant conductance or resistance circles (since we add only idealized inductors or capacitors to result in a matched condition) - so that explains it for LC - but still confused with stub matching. please explain

if my question is not clear, please let me know.

Matching with stubs involves moving along the length of the TL. The input impedance of the TL as the distance is varied from 0 (the load) to lamda/2 happens to be on a circle whose radius is the reflection coffecient. Hence we have to move along the SWR circle which is known once the magnitude of reflection coeff is known. I answered my own question.

any further inputs or thoughts are welcome.