OCR MEI Further Pure Core 2024 June — Question 12

Exam BoardOCR MEI
ModuleFurther Pure Core (Further Pure Core)
Year2024
SessionJune
TopicHyperbolic functions

12 The diagram shows the curve with parametric equations \(x = 2 \cosh t + \sinh t , y = \cosh t - 2 \sinh t\).
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  1. The curve crosses the positive \(x\)-axis at A .
    1. Determine the value of the parameter \(t\) at A , giving your answer in logarithmic form.
    2. Find the \(x\)-coordinate of A , giving your answer correct to \(\mathbf { 3 }\) significant figures.
  2. The point B has parameter \(t = 0\). Determine the equation of the tangent to the curve at B .