A-LevelMathematicsCoordinate geometry9709/12 · Oct/Nov 2011 · Q47 Marks
The equation of a curve is y² + 2x = 13 and the equation of a line is 2y + x = k, where k is a constant.
- (i)In the case where k = 8, find the coordinates of the points of intersection of the line and the curve.[4]
- (ii)Find the value of k for which the line is a tangent to the curve.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.
- [4] y² - 4y + 3 = 0
- [4] (2, 3)
- [4] (6, 1)
- [3] y² + 2(k – 2y) = 13
- [3] Uses b² - 4ac on “quadratic = 0)
- [3] k = 8½
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