Operation of LC circuit in Frequency Modulation with simulation and linking it to the basic principle of frequency modulation
Inside the BJT is the miller capacitor and this capacitor (for AC signals) can be shown to be effectively in parallel with the tank circuit. The miller capacitor can be altered by the application of different base-collector voltages hence a signal on the base can dynamically change the miller capacitor and cause the carrier frequency to become modulated with the audio signal. It's not a great FM circuit but it does work with some distortion on the demodulated signal.