O-LevelAdditional MathematicsEquations, inequalities and graphs4037/12 · May/June 2025 · Q38 Marks
A circle with centre C has the equation x²+y² - 10x-4y+24 = 0.
- (a)Show that the line y = 2x-3 is a tangent to this circle.[3]
- (b)Given that this tangent touches the circle at the point P, find the coordinates of P.[2]
- (c)Find the equation of the circle which has its centre at P and passes through the origin.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [M1] 5x²-30x+45 (=0) or equivalent 3 term quadratic (for attempt to eliminate one variable)
- [A1] Use of discriminant or solution to show one repeated root or a single solution (Must have conclusion e.g. Discriminant = 0 (so tangent) oe One solution only (so tangent))
- [B1] (3, 3) (B1 for each coordinate)
- [B1] Radius = 3√2 oe soi
- [B1] (x-3)²+(y-3)² soi (FT on their answer to (b) only)
- [B1] (x-3)² +(y-3)² =18 oe (ISW any expansion)
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