MPM2D Equation of a Circle Worksheet
1. Which of the following is the equation of a circle with centre at (0, 0)
and a radius of 5 units?
a) x + y = 5
b) x2 + y2 = 5
c) x2 + y2 = 25
d) x2 – y2 = 25
2. Which of the following is the equation of a circle with centre at (0, 0)
and a radius of 74 units?
4
16
16
4
a) x2 + y2 =
b) x2 + y2 =
c) x2 – y2 =
d) x + y =
7
49
49
7
3. Which of the following is the equation of a circle with centre at (0, 0)
and a diameter of 12 units?
a) x2 + y2 = 144
b) x2 + y2 = 12
c) x2 – y2 = 36
d) x2 + y2 = 36
4. Which of the following is the equation of a circle with centre at (0, 0)
and a diameter of 22 units?
a) x2 + y2 = 121
b) x2 + y2 = 484
c) x2 + y2 = 22
d) x2 + y2 = = 11
5. Which of the following is the equation of a circle with centre at (0, 0)
and an x-intercept of –8?
a) x2 + y2 = –8
b) x2 + y2 = 64
c) x2 + y2 = 16
d) x2 + y2 = –16
6. Which of the following is CORRECT for the circle x2 + y2 = 169?
a) The x-intercept is –13 and the radius is 14 units.
b) The y-intercept is at (13, 0) and the radius is 13 units.
c) The x-intercepts are at (±13, 0) and the radius is 169 units.
d) The y-intercepts are at (0, ±13) and the radius is 13 units.
7. What is the radius of a circle with centre at (0, 0) that passes through
(–8, –15)?
a) 17 units b) 8 units c) 15 units d) 289 units
8. What is the radius of a circle with centre at (0, 0) that passes through
(–14, 48)?
a) 48 units b) 50 units c) 14 units d) 2500 units
9. Which of the following points is on a circle with centre at (0, 0) and a
radius of 5 units?
a) (–3, 5) b) (0, 25) c) (–4, 3) d) (5, –5)
10. State the equation of a circle with centre at (0, 0) that passes through
(–7, 8).
11. State the equation of a circle with centre at (0, 0) and a diameter of
36 units.
12. State the equation of a circle with centre (0, 0) that passes through (–
12, 19).
13. For each of the given points, determine whether it is on, inside, or
outside the circle x2 + y2 = 256.
a) (–13, 8)
b) (–16, 0)
c) (10, 13)
14. A circle with centre at (0, 0) has an x-intercept at (11, 0). State the
coordinates of the y-intercepts of the circle.
15. A circle with centre at (0, 0) passes through (–16, 12). State the
radius of the circle.
16. A sprinkler rotates in a circular path and it sprays water out to a
maximum of 4 m from the sprinkler head. Write the equation of a graph
that models this situation.
17. A square concrete patio is being constructed so that it will contain a
contrasting circular interlocking brick design. If the diagonal of the
square measures 16√2 units, what is the equation of the largest circle
that can fit inside the square? Explain your solution.
18. Two satellites are orbiting Mars. The path of one satellite is
represented by the equation x2 + y2 = 1 440 000 and the path of the
second satellite is represented by the equation x2 + y2 = 1 822 500. All
distances are recorded in kilometres. In one orbit, how many more
kilometres does the second satellite travel than the first one? Show the
steps of your solution.