A family of slope fields is generated by the differential equation dxdy=y2−c, where c is a positive constant. Students compare slope fields for c=1, c=4, and c=9. Which statement best describes how the positions and stability of equilibrium solutions change as c increases?
a) The two equilibrium lines move closer to the x-axis, but their stability types remain unchanged.
b) The two equilibrium lines move farther from the x-axis, and both become stable.
c) The two equilibrium lines move farther from the x-axis, but their stability types remain unchanged.
d) The lower equilibrium line disappears for c>1, leaving only a single equilibrium line above the x-axis.