If you have a curvilinear relationship, then: (Hint: The two most important sources of bias in this context are probably linearity and normality.)

a. It is not appropriate to use Pearson's correlation because it assumes a linear relationship between variables.
b. Pearson's correlation can be used in the same way as it is for linear relationships.
c. You can use Pearson's correlation; you just need to remember that a curve indicates that the variables are not linearly related.
d. Transforming the data won't help.