Why A reactance modulator presents a variable reactance, typically an effective capacitance (often a varactor diode whose junction capacitance changes with applied audio voltage), across an oscillator's tank circuit. Since the oscillator frequency depends on L and C, varying that capacitance at an audio rate swings the carrier frequency or phase, producing FM or PM. Angle modulation comes from changing the resonant elements, not the signal amplitude.
Watch out The choices built on varying a resistance are wrong because resistance is not reactance; loading a tank with changing resistance alters amplitude and Q rather than shifting the resonant frequency. AM is produced by varying gain or supply level in an amplifier stage, not by a reactance modulator.
Reactance means L or C. Change C, change frequency: reactance modulator gives FM/PM, never AM.