A-LevelMathematicsCoordinate geometry9709/12 · Feb/Mar 2021 · Q87 Marks
The points A (7, 1), B (7, 9) and C (1, 9) are on the circumference of a circle.
- (a)Find an equation of the circle.[5]
- (b)Find an equation of the tangent to the circle at B.[2]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2021). The mark or mark type is shown in brackets.
- [2] Centre of circle is (4, 5)
- [1] r² = (7-4)²+(1-5)² (OE. Either using their centre and A or C or using A and C and dividing by 2.)
- [1] r = 5 (FT on their (4, 5) if used.)
- [1] Equation is (x-4)² + (y − 5)² = 25 (OE. Allow 5² for 25.)
- [1] Gradient of radius = (9-5)/(7-4) = 4/3 (FT for use of their centre.)
- [1] Equation of tangent is y -9 = -3/4(x-7) (or y = -3x/4 + 57/4)
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