Questions — Edexcel AS Paper 1 (152 questions)

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Edexcel AS Paper 1 Q14
11 marks Standard +0.3
A curve with centre \(C\) has equation $$x^2 + y^2 + 2x - 6y - 40 = 0$$
    1. State the coordinates of \(C\).
    2. Find the radius of the circle, giving your answer as \(r = n\sqrt{2}\). [3]
  2. The line \(l\) is a tangent to the circle and has gradient \(-7\). Find two possible equations for \(l\), giving your answers in the form \(y = mx + c\). [8]
Edexcel AS Paper 1 Q15
Challenging +1.2
\includegraphics{figure_5} Figure 5 shows a sketch of part of the curve \(y = 2x + \frac{8}{x^2} - 5\), \(x > 0\). The point \(A(4, \frac{7}{2})\) lies on C. The line \(l\) is the tangent to C at the point A. The region \(R\), shown shaded in figure 5 is bounded by the line \(l\), the curve C, the line with equation \(x = 1\) and the \(x\)-axis. Find the exact area of \(R\). (Solutions based entirely on graphical or numerical methods are not acceptable.)