For a fixed A R, define the curve C in R2 by the equation y-2xy = x +Ax + 4. You can view this family of curves on Desmos. Note this demo will not help you justify your answers below. (2a) Prove that if A #-6 and A # 6, then C is a regular curve. You may use WolframAlpha to solve a 1-variable quartic equation. (2b) This family of curves can instead be viewed as the z-slices of the surface S in R defined by the equation y-2xy = x+xz +4 Use the implicit function theorem to show that this equation defines a 2-dimensional regular surface (2c) The curves C, and C_6 are regular at each point except (-1,-1) and (1,1) respectively. These points where C6 and C_6 fail to be regular are called singularities. View this surface and family of curves on Math3d. (Google Chrome is the most stable browser for Math3D.) Informally explain how the shape of the surface appears to relate to the singularities of C6 and C_6. Your explanation must discuss both the surface and the curves.