5 Josh and Zoe are solving the following mathematics problem: The curve \(C _ { 1 }\) has equation $$\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$$ The matrix \(\mathbf { M } = \left[ \begin{array} { l l } 0 & 1
1 & 0 \end{array} \right]\) maps \(C _ { 1 }\) onto \(C _ { 2 }\)
Find the equations of the asymptotes of \(C _ { 2 }\) Josh says that to solve this problem you must first carry out the transformation on \(C _ { 1 }\) to find \(C _ { 2 }\), and then find the asymptotes of \(C _ { 2 }\) Zoe says that you will get the same answer if you first find the asymptotes of \(C _ { 1 }\), and then carry out the transformation on these asymptotes to obtain the asymptotes of \(C _ { 2 }\) Show that Zoe is correct.