Edexcel IAL P2 Circles Questions
Equation of a circle in Cartesian form, tangent-radius perpendicularity, geometric problem solving.
- P2 · Pure Mathematics 2
- Calculator allowed
- 45 practice questions
What the questions test
The 45 P2 circles practice questions cover:
Worked example 1
The points $A(1, 2)$ and $B(7, 10)$ lie on a circle $C$ with $AB$ as a diameter.
(a) Find the equation of $C$. (4)
(b) The tangent to $C$ at $A$ meets the $y$-axis at $T$. Find the coordinates of $T$. (3)
Mark scheme
(a) Centre $=$ midpoint $= (4, 6)$ B1. Radius $= \tfrac12|AB| = \tfrac12\sqrt{36+64} = 5$ M1 A1. Equation: $(x-4)^2 + (y-6)^2 = 25$ A1.
(b) Radius from centre to $A$ has gradient $\tfrac{2-6}{1-4} = \tfrac{4}{3}$ B1. Tangent gradient $= -\tfrac{3}{4}$; equation: $y - 2 = -\tfrac{3}{4}(x - 1)$. Set $x = 0$: $y = 2 + \tfrac{3}{4} = \tfrac{11}{4}$ M1 A1.
Worked example 2
The circle $C$ has centre $(a, b)$ and passes through the points $P(0, 0)$, $Q(6, 0)$, and $R(0, 8)$. Find the values of $a$, $b$, and the radius of $C$.
Mark scheme
$P$ and $Q$ both on circle ⇒ centre lies on the perpendicular bisector of $PQ$, so $a = 3$ M1 A1. Similarly $P$ and $R$ give $b = 4$ M1 A1. Radius $= |CP| = \sqrt{9 + 16} = 5$ M1 A1.
FAQ
What circles is in Edexcel IAL P2?
Equation of a circle in Cartesian form, tangent-radius perpendicularity, geometric problem solving.
Is P2 a calculator paper?
Yes, a calculator is allowed in P2, but method marks are only given for working you write down.
How are P2 circles questions marked?
With M marks for a correct method, A marks for accurate answers that depend on the M mark before them, and B marks for independent results, as in the worked examples on this page.