6．（a）Given that \(x ^ { 4 } + y ^ { 4 } = 1\) ，prove that \(x ^ { 2 } + y ^ { 2 }\) is a maximum when \(x = \pm y\) ，and find the maximum and minimum values of \(x ^ { 2 } + y ^ { 2 }\) ．
（b）On the same diagram，sketch the curves \(C _ { 1 }\) and \(C _ { 2 }\) with equations \(x ^ { 4 } + y ^ { 4 } = 1\) and \(x ^ { 2 } + y ^ { 2 } = 1\) respectively．
（c）Write down the equation of the circle \(C _ { 3 }\) ，centre the origin，which touches the curve \(C _ { 1 }\) at the points where \(x = \pm y\) ．