2024 NYJC H1 Q4

The curve \(D\) has equation \(y = -\ln(2x^2 - x + 1)\). \(D\) crosses the positive \(x\)-axis at \(A\).

1. Use a non-calculator method to find the equation of the tangent to \(D\) at \(A\) in the form \(ax + by = c\), where \(a\), \(b\) and \(c\) are integers to be found.[4]
2. Sketch the graphs of \(D\) and the tangent found in part (a) on a single diagram, stating the exact coordinates of the points of intersection with the axes.[2]
3. \(R\) is the finite region bounded by the curve \(D\), the tangent in part (b) and the \(y\)-axis. Find the area of \(R\), giving your answer correct to \(2\) decimal places.[2]