A-LevelMathematicsCoordinate geometry9709/12 · Oct/Nov 2016 · Q56 Marks
The line x/a + y/b = 1, where a and b are positive constants, intersects the x- and y-axes at the points A and B respectively. The mid-point of AB lies on the line 2x + y = 10 and the distance AB = 10. Find the values of a and b.
- The line x/a + y/b = 1, where a and b are positive constants, intersects the x- and y-axes at the points A and B respectively. The mid-point of AB lies on the line 2x + y = 10 and the distance AB = 10. Find the values of a and b.[6]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2016). The mark or mark type is shown in brackets.
- [B1] A(a, 0) and B (0, b) soi
- [M1*] Uses Pythagoras with their A & B.
- [B1^] M has coordinates (a/2, b/2) on their A and B.
- [M1*] Subs into given line, using their M, to link a and b.
- [DM1] Forms quadratic in a or in b.
- [A1] → a = 6, b = 8. cao
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