Answer
290 pF
Work Step by Step
Equation 21-19 gives the resonant frequency of a LC circuit. Assume that the inductance L stays the same. Applying that equation, consider the ratio of the two frequencies, and cancel out like terms. Let “1” designate the station at 550 kHz.
$$\frac{f_1}{f_2}=\sqrt{\frac{C_2}{C_1}}$$
$$C_2=C_1(\frac{f_1}{f_2})^2$$
$$=(2500pF)(\frac{550kHz}{1610kHz})^2=290pF$$
