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A-LevelMathematicsCoordinate geometry9709/12 · Oct/Nov 2012 · Q46 Marks

The line y = x/k + k, where k is a constant, is a tangent to the curve 4y = x² at the point P.

  1. (i)find the value of k,[3]
  2. (ii)the coordinates of P.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2012). The mark or mark type is shown in brackets.

  1. [M1] Eliminates x or y completely (e.g., substitute y from line into curve)
  2. [M1] Uses b² - 4ac = 0 for a quadratic
  3. [A1] → k = -1
  4. [M1] Elimination of x or y (substituting k=-1 into line and curve equations)
  5. [M1] Soln of eqn. co. (for the coordinates)
  6. [A1] → P(-2, 1)

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About this question

Topic
Coordinate geometry, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, Oct/Nov 2012 Paper 1 Variant 2, question 4.

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