2025 TJC P1 Q9

2025 TJC P1 Q9

11 marks

A curve \(C\) is defined parametrically by the equations

\[x = t + \frac{1}{t}, \quad y = t - \frac{1}{t}, \quad t \neq 0.\]

  1. Sketch the curve \(C\), showing clearly the coordinates of the axial intercepts.[2]
  2. Use differentiation to find the values of \(t\) for which the tangents to the curve are parallel to the \(y\)-axis.[3]
  3. Show that the equation of normal at the point where \(t = 2\) is given by \(y = -\frac{3}{5}x + 3\).[3]
  4. The normal at the point where \(t = 2\) cuts the curve \(C\) again at the point \(Q\). Determine the exact coordinates of \(Q\).[3]
Finding similar questions...
Answer:(b)\(t=\pm 1\) (d)coordinates of Q : (\(-\frac{65}{8},\frac{63}{8})\)

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