A-level · Coordinate geometry

The equation of a circleExam-style questions

Why (x − a)² + (y − b)² = r² is just the distance formula squared, reading the centre and radius off it, and completing the square to recover them from the expanded form x² + y² + 2gx + 2fy + c = 0.

Start practising Read the lesson

26 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
A circle has centre $C(1,3)$ and passes through the point $P(4,7)$ .
(a) Find the equation of the circle. (2 marks)
(b) Find the equation of the tangent to the circle at $P$ , giving your answer in the form $ax + by = c$ , where $a$ , $b$ and $c$ are integers. (3 marks)
Level 2 · 5 marksTry it
2
A circle $C$ has equation

$x^2 + y^2 + 10kx - 4ky + 9 = 0$

where $k$ is a constant.

Find, in terms of $k$ ,

(i) the coordinates of the centre of $C$

(ii) the radius of $C$

(3 marks)
Level 2 · 3 marksTry it