5 A curve is defined by the parametric equations
$$x = 8 t ^ { 2 } - t , \quad y = \frac { 3 } { t }$$
- Show that the cartesian equation of the curve can be written as \(x y ^ { 2 } + 3 y = k\), stating the value of the integer \(k\).
(2 marks) - Find an equation of the tangent to the curve at the point \(P\), where \(t = \frac { 1 } { 4 }\).
- Verify that the tangent at \(P\) intersects the curve when \(x = \frac { 3 } { 2 }\).