Show that if a surface is given in the forn z=(x, y),then the measure of curvature k can be expressed as k=(z_xxz_yy -( z_xy)^2)/(1+ (z_x)^2 +(z_y)^2)^2 hint show first that if X, Y, Z are coordinates on the unit sphere correspobdibg to the point (x, y, z(x, y)) on the given surface then, X= (-z_x)/square root(1+(z_x)^2 +(z_y)^2, Y = (-z_y)/squareroot (1+(z_x)^2 +(z_y)^2) Z= 1/ squar root (1+(z_x)^2 +(z_y)^2)