A-LevelMathematicsCoordinate geometry9709/12 · Oct/Nov 2020 · Q99 Marks
A circle has centre at the point B (5, 1). The point A (−1, –2) lies on the circle.
- (a)Find the equation of the circle.[3]
- (b)Point C is such that AC is a diameter of the circle. Point D has coordinates (5, 16). Show that DC is a tangent to the circle.[4]
- (c)The other tangent from D to the circle touches the circle at E. Find the coordinates of E.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [B1] r = √((6² + 3²)) or r² = 45 Sight of r = 6.7 implies B1
- [M1] Using centre given and their radius or r in correct formula
- [A1] (x - 5)² + (y - 1)² = 45 or x² −10x + y² – 2y = 19 Do not allow (√45)² for r²
- [B1] C has coordinates (11, 4)
- [B1] 0.5 OE, Gradient of AB, BC or AC.
- [M1] Calculation of gradient needs to be shown for this M1.
- [A1] Clear reasoning needed.
- [B1] E (-1, 4)
- [B1] for each coordinate
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