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This cap may not be needed if your low-dropout regulator is driven by a voltage source having a very small internal impedance and placed very close to its input. Therefore, a cap is just a solution when the previous case couldn't be implemented.
Now, if one needs to know why at the input (and at the output perhaps) a low impedance helps stabilizing the function of the regulator, the internal circuit of the regulator should be analyzed more in detail.
Thanks for your attention and answering the issue.
I am explaining the situation i have seen. I have 5 v supply through which i am feeding input to two different LDOs connected parallel to it.at the output of capacitor, I see 47 uF shunt cap ( case C, 10 V) and after parallel connections to LDO, just before LDOs, 10 uF caps are there which is nothing but LDO input cap. similar cap at LDO output.
Can you please tell me the role of each cap in the picture i described
Shunt capacitances at input and output stages in power circuits(either linear or smps) are generally used for lowpass filtering that filters out undesired ripple. Furthermore, I have experienced that some shunt capacitances around a LDO regulator may have important role in internal control mechanisms of the LDOs. If you dont put that cap there, you will see output voltage shifts to somewhere being far from your expectation.
As KerimF mentioned, you need to investigate your LDO's datasheet to understand roles of the caps. However, manufacturers may not give detailed information but there must be recommended application circuits, stick those schematics.