To find the points of intersection, substitute \(y = 11 - 2x\) from the line equation into the curve equation \(xy = 12\).

Substitute: \(x(11 - 2x) = 12\).

Expand and rearrange: \(11x - 2x^2 = 12\).

Rearrange to form a quadratic equation: \(2x^2 - 11x + 12 = 0\).

Factor the quadratic: \((2x - 3)(x - 4) = 0\).

Solve for \(x\): \(x = \frac{3}{2}\) or \(x = 4\).

Substitute back to find \(y\):

For \(x = \frac{3}{2}\), \(y = 11 - 2 \times \frac{3}{2} = 8\).

For \(x = 4\), \(y = 11 - 2 \times 4 = 3\).

Thus, the points of intersection are \(\left( \frac{1}{2}, 8 \right)\) and \((4, 3)\).