What type of FM detector is preceded by a tank circuit?

A slope detector utilizes a tank circuit, which is a resonant circuit tuned to the frequency of the incoming FM signal. This type of detector converts frequency variations in the modulated signal into amplitude variations, which can then be demodulated. The tank circuit helps to narrow the bandwidth, allowing the detector to more effectively respond to changes in frequency, thus enhancing its performance for demodulating FM signals. The slope of the frequency response curve in the vicinity of the tank circuit's resonance is what enables the conversion from frequency to amplitude, making it particularly suited for detecting FM signals. This is why the slope detector is the correct choice in this scenario.