A-LevelMathematicsCoordinate geometry9709/12 · Feb/Mar 2019 · Q1012 Marks
The diagram shows the curve with equation y = 4x^(1/2). [Figure X.X]
- (i)The straight line with equation y = x + 3 intersects the curve at points A and B. Find the length of AB.[6]
- (ii)The tangent to the curve at a point T is parallel to AB. Find the coordinates of T.[3]
- (iii)Find the coordinates of the point of intersection of the normal to the curve at T with the line AB.[3]
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Mark scheme
Marking points from the official mark scheme (Feb/Mar 2019). The mark or mark type is shown in brackets.
- [M1] 4x½ = x +3→
- [A1] x½ = 1 or 3
- [A1] x = 1 or 9
- [A1ft] y = 4 or 12
- [M1] AB² = (9-1)² + (12-4)²
- [A1] AB = √128 or 8√2 oe or 11.3
- [B1] dy/dx = 2x⁻¹/²
- [M1] 2x⁻¹/² = 1
- [A1] (4, 8)
- [M1] Equation of normal is y-8=-1(x-4)
- [M1] Eliminate y (or x) → −x+12 = x + 3 or y-3=12-y
- [A1] (4½, 7½)
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