Given that \(14 x ^ { 2 } - 7 x y + y ^ { 2 } = 2\), show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 28 x - 7 y } { 7 x - 2 y }\).
The points \(L\) and \(M\) on the curve \(14 x ^ { 2 } - 7 x y + y ^ { 2 } = 2\) each have \(x\)-coordinate 1 . The tangents to the curve at \(L\) and \(M\) meet at \(N\). Find the coordinates of \(N\).