1. A switching power supply comprising: a resonant circuit including a capacitor and a coil coupled to the capacitor; a switching circuit including a switching element and configured to supply a voltage to the resonant circuit; a smoothing circuit configured to smooth a voltage output from the resonant circuit and outputs an output voltage; a resonance controller configured to, when a control instruction signal is input cause the switching element to be turned on and off at a first frequency in such a manner that the output voltage becomes a specific voltage, the control instruction signal indicating to control the switching circuit; and a controller configured to discontinuously output the control instruction signal to the resonance controller at a second frequency being lower than the first frequency after an operation instruction signal is input until the output voltage becomes higher than a threshold voltage, and continuously output the control instruction signal to the resonance controller after the output voltage becomes higher than the threshold voltage until the operation instruction signal is not input, the operation instruction signal indicating to perform an operation.