A-LevelMathematicsCoordinate geometry9709/12 · Feb/Mar 2022 · Q68 Marks
The circle with equation (x + 1)² + (y − 2)² = 85 and the straight line with equation y = 3x – 20 are shown in the diagram. The line intersects the circle at A and B, and the centre of the circle is at C. [Figure 6.1]
- (a)Find, by calculation, the coordinates of A and B.[4]
- (b)Find an equation of the circle which has its centre at C and for which the line with equation y = 3x - 20 is a tangent to the circle.[4]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2022). The mark or mark type is shown in brackets.
- [M1] (x+1)² + (3x-22)² = 85
- [A1] 10x²-130x+400 [=0]
- [A1] [10](x-8)(x-5) leading to x = 8 or 5
- [A1] (8, 4), (5, -5)
- [M1] Mid-point of AB = (6½, -½)
- [B1 SOI] Use of C = (-1, 2)
- [M1] r² = (-1 - 6½)² + (2 - (-½))²
- [A1] Equation of circle is (x + 1)² + (y − 2)² = 62½
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