yzr2 2 (a) Draw contour lines for f{;r,y) and grime] in a single Iyplane and single tur plane respectively. These should correspond to f = , 1_~ 1_.2_. 2_. 31 3 and g = {L 1, -1._ 2, -2, 3. 3 and any axes-intercepts should be clearly marked. 2. Consider f{:r1y] = and ghee] = as. {h} At what points and for which c, do the lines L-' = s. and s = u cross the contour g = c? At what distance from the origin do these intersections occur'.' (c) At what points and for which e' do the lines J: = and y = I] cross the contour f = o'.' At what distance from the origin do these intersections occur? {d} The above work suggests a geometric transformation will transform the graph of f to the graph of 9*. You could use a 3D graphed such as that available from the MATHIHEI} Canvas site, to convince yourself further. Say the transformation is u = T1{J:,y} and i: = T2{I1y}. Find functions T] and T2 that honour this transformation where to preserve symmetry require the distances from the origin to be equal. In other words~ require V's: + y = u\" 1:2 + 192. or simply .122 +312 2 a? +tl2