O-LevelAdditional MathematicsStraight line graphs4037/11 · May/June 2025 · Q36 Marks
Point A has coordinates (3, -1). A circle has equation (x-4)² + (y+3)² = 5.
- (a)Show that A lies on the circumference of the circle.[1]
- (b)Given that AB is a diameter of the circle, find the coordinates of B.[2]
- (c)Find the equation of the tangent to the circle at A.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [B1] (3-4)² + (-1+3)² = 5 or showing that distance between point A and centre of circle = radius e.g. √( (3-4)² + (-1+3)² ) = √5
- [M1] Award M1 for the 2 equations (3+x)/2 = 4 and (-1+y)/2 = -3
- [A1] (5, -5)
- [M1] gradient of radius = (-3+1)/(4-3) = -2 soi by gradient of tangent
- [M1] FT their -2; gradient of tangent = -1/their(-2)
- [A1] y + 1 = 1/2 (x - 3) oe
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