Leaving Cert Maths: Coordinate geometry: circle
How often Coordinate geometry: circle comes up on the Maths papers, every year it was asked, and questions to try.
HL Asked on 10 of the last 10 Higher Level papers, most recently in 2026. banker
OL Asked on 10 of the last 10 Ordinary Level papers, most recently in 2026. banker
Quick ones on Coordinate geometry: circle.
- (−2, 5)
- (2, −5)
- (2, 5)
- 24.5
- 49
- 7
- √(g² + f² − c)
- g² + f² − c
- √(g² + f² + c)
Show the answers
(a) (2, −5)
(b) 7
(c) √(g² + f² − c)
Higher Level
Asked on 10 of the last 10 Higher Level papers, most recently in 2026. banker
Every paper, year by year
| Year | Where it came up |
|---|---|
| 2026 | Q5 |
| 2025 | Q2, Q7 |
| 2024 | Q5, Q9 |
| 2023 | Q4, Q9 |
| 2022 | Q3 |
| 2021 | Q3 |
| 2019 | Q3 |
| 2018 | Q5 |
| 2017 | Q4 |
| 2016 | Q2 |
Links open the State Examinations Commission’s paper for that year.
More Coordinate geometry: circle questions
Coordinate geometry: circle, 2 marks
Circle with centre (1, 2) and radius 3?
- (x + 1)² + (y + 2)² = 9
- (x − 1)² + (y − 2)² = 3
- (x − 1)² + (y − 2)² = 9
Show the answer
(x − 1)² + (y − 2)² = 9
(x − h)² + (y − k)² = r² with h = 1, k = 2 and r² = 3² = 9.
Coordinate geometry: circle, 2 marks
Radius of x² + y² − 6x − 8y = 0?
- 25
- 5
- 10
Show the answer
5
g = −3, f = −4, c = 0, so r = √(g² + f² − c) = √(9 + 16) = √25 = 5.
Coordinate geometry: circle, 2 marks
A line that meets a circle at exactly one point is a …
- tangent
- chord
- diameter
Show the answer
tangent
A tangent just touches the circle at one point. A line through two points of the circle is a secant.
Ordinary Level
Asked on 10 of the last 10 Ordinary Level papers, most recently in 2026. banker
Every paper, year by year
| Year | Where it came up |
|---|---|
| 2026 | Q7 |
| 2025 | Q3 |
| 2024 | Q4 |
| 2023 | Q2 |
| 2022 | Q2 |
| 2021 | Q4 |
| 2019 | Q4 |
| 2018 | Q4 |
| 2017 | Q2 |
| 2016 | Q3 |
Links open the State Examinations Commission’s paper for that year.
More Coordinate geometry: circle questions
Coordinate geometry: circle, 2 marks
What is the radius of the circle x² + y² = 49?
- 49
- 24.5
- 7
Show the answer
7
For x² + y² = r² we have r² = 49, so the radius is √49 = 7.
Coordinate geometry: circle, 2 marks
What is the centre of the circle x² + y² = 25?
- (25, 25)
- (0, 0)
- (5, 5)
Show the answer
(0, 0)
A circle written as x² + y² = r² is always centred on the origin (0, 0). Here the radius is 5.
Coordinate geometry: circle, 2 marks
Write the equation of the circle with centre (0, 0) and radius 6.
- x² + y² = 36
- x² + y² = 6
- x² + y² = 12
Show the answer
x² + y² = 36
The form is x² + y² = r², and r² = 6² = 36.