Studies of patterns of abundance enhancements of elements, relative to solar coronal abundances, in large solar energetic-particle (SEP) events, and of their power-law dependence on the mass-to-charge ratio, A/Q, of the ions, have been used to determine the effective source-plasma temperature, T, that defines the Q-values of the ions. We find that a single assumed value for the coronal reference He/O ratio in all SEP events is often inconsistent with the transport-induced power-law trend of the other elements. In fact, the coronal He/O varies rather widely from one SEP event to another. In the large Fe-rich SEP events with T approximate to 3 MK, where shock waves, driven out by coronal mass ejections (CMEs), have reaccelerated residual ions from impulsive suprathermal events that occur earlier in solar active regions, He/O approximate to 90, a ratio similar to that in the slow solar wind, which may also originate from active regions. Ions in the large SEP events with T < 2 MK may be accelerated outside active regions, and have values of 40 <= He/O <= 60. Mechanisms that determine coronal abundances, including variations of He/O, are likely to occur near the base of the corona (at approximate to 1.1 R-S) and thus to affect both SEPs (at 2-3 R-S) and the solar wind. Other than He, reference coronal abundances for heavier elements show little temperature dependence or systematic difference between SEP events; He, the element with the highest first-ionization potential, is unique. The CME-driven shock waves probe the same regions of space, at approximate to 2 R-S near active regions, which are also likely sources of the slow solar wind, providing complementary information on conditions in those regions.