Q.In a Colpitt's oscillator circuit :

The Colpitts oscillator's tank circuit uses a capacitive voltage-divider (two series capacitors with a single inductor) to derive its feedback signal, which is why it is characterised as using capacitive feedback.

An LC oscillator sustains continuous oscillation by feeding a fraction of the tank circuit's output signal back to the amplifying device (transistor or op-amp) in the correct phase to satisfy the Barkhausen criterion (loop gain $\ge 1$, loop phase shift $=0°$ or a multiple of $360°$). Different LC-oscillator topologies differ mainly in how this feedback fraction is tapped from the tank circuit.

In a Colpitts oscillator, the tank circuit consists of a single inductor $L$ in parallel with two capacitors $C_1$ and $C_2$ connected in series with each other. The junction between $C_1$ and $C_2$ forms a capacitive voltage divider, and the feedback voltage fed back to the amplifier's input is tapped from this junction — hence 'capacitive feedback'. The oscillation frequency is set by $L$ and the series combination of $C_1,C_2$: $f=\dfrac{1}{2\pi\sqrt{LC_{eq}}}$ with $C_{eq}=\dfrac{C_1 C_2}{C_1+C_2}$.

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