3.8 Understand that (x – a)^2 + (y – b)^2 = r^2 is the equation of a circle with centre (a, b) and radius r Quiz: AQA Further Maths, Unit 3

The 20 questions

1. What are the centre and radius of (x - 2)^2 + (y + 3)^2 = 16?

   • Centre (2, -3), radius 16
   • Centre (2, -3), radius 4
   • Centre (2, 3), radius 16
   • Centre (-2, 3), radius 4

2. Which is the equation of a circle with centre (1, 5) and radius 2?

   • (x - 1)^2 + (y - 5)^2 = 16
   • (x + 1)^2 + (y + 5)^2 = 4
   • (x - 1)^2 + (y - 5)^2 = 4
   • (x - 1)^2 + (y - 5)^2 = 2

3. Which point is the centre of (x + 4)^2 + (y - 1)^2 = 9?

   • (-4, 1)
   • (-4, -1)
   • (4, -1)
   • (4, 1)

4. What is the radius of the circle (x - 3)^2 + (y - 2)^2 = 25?

   • 12.5
   • 5
   • 625
   • 25

5. Does the point (5, 2) lie on the circle (x - 2)^2 + (y - 2)^2 = 9?

   • Cannot be determined
   • No
   • Yes
   • Only if x = 0

6. Which circle has centre (3, 0) and radius 2?

   • (x - 3)^2 + y^2 = 16
   • (x - 3)^2 + y^2 = 2
   • (x + 3)^2 + y^2 = 4
   • (x - 3)^2 + y^2 = 4

7. In the circle equation (x - a)^2 + (y - b)^2 = r^2, what does (a, b) represent?

   • Y-intercept
   • Point on circle
   • Centre of circle
   • Radius of circle

8. A circle has centre (4, -2) and passes through (4, 3). What is its radius?

   • 5
   • 25
   • 7
   • 1

9. Which circle has centre (-1, 2) and passes through the origin?

   • (x + 1)^2 + (y - 2)^2 = 4
   • (x + 1)^2 + (y - 2)^2 = 8
   • (x + 1)^2 + (y - 2)^2 = 5
   • (x - 1)^2 + (y + 2)^2 = 5

10. Find the centre and radius of x^2 + y^2 - 6x + 4y - 3 = 0.

    • Centre (3, -2), radius 4
    • Centre (3, -2), radius 3
    • Centre (3, -2), radius sqrt(13)
    • Centre (-3, 2), radius 4

11. A circle has centre (2, 3) and radius 4. Where is the point (6, 6)?

    • Inside the circle
    • On the circle
    • At the centre
    • Outside the circle

12. The circle (x - 5)^2 + (y + 1)^2 = 49 has which lowest point?

    • (5, -8)
    • (5, 6)
    • (12, -1)
    • (-2, -1)

13. What do circles sharing the same centre but different radii are called?

    • Tangent
    • Orthogonal
    • Parallel
    • Concentric

14. The circle (x - 3)^2 + (y - 4)^2 = r^2 passes through (0, 0). Find r^2.

    • 12
    • 5
    • 25
    • 7

15. Which equation describes the circle with diameter AB where A(0, 0) and B(6, 8)?

    • (x - 3)^2 + (y - 4)^2 = 25
    • (x - 6)^2 + (y - 8)^2 = 100
    • (x - 3)^2 + (y - 4)^2 = 100
    • (x + 3)^2 + (y + 4)^2 = 25

16. Complete the square for x^2 + y^2 + 4x - 2y - 4 = 0. What are the centre and radius?

    • Centre (-2, 1), radius 9
    • Centre (2, -1), radius 3
    • Centre (-2, 1), radius sqrt(5)
    • Centre (-2, 1), radius 3

17. Which point lies on (x - 2)^2 + (y - 1)^2 = 10?

    • (4, 4)
    • (5, 1)
    • (2, 4)
    • (5, 2)

18. A circle has centre (3, -1) and passes through (6, 3). What is its radius?

    • 25
    • 4
    • 7
    • 5

19. A circle with centre (2, b) and radius 3 touches the x-axis from above. Find b.

    • 3
    • 6
    • -3
    • 9

20. Which circle has centre (0, 3) and passes through (4, 0)?

    • (x - 3)^2 + y^2 = 25
    • x^2 + (y - 3)^2 = 16
    • x^2 + (y + 3)^2 = 25
    • x^2 + (y - 3)^2 = 25

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