Lesson C2

C2 Circles in coordinate geometry Quiz: AQA Maths, Unit 3

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson C2, Circles in coordinate geometry: 20 multiple choice questions for the AQA Maths (7357), Unit 3: Coordinate geometry, written with Revision Ninja.

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The 20 questions

  1. What is the standard equation of a circle with centre (a, b) and radius r?

    • (x - a)^2 - (y - b)^2 = r^2
    • (x - a)^2 + (y - b)^2 = r^2
    • (x + a)^2 + (y + b)^2 = r^2
    • (x - a)^2 + (y - b)^2 = r

  2. What is the angle in a semicircle?

    • Equal to the angle at the centre
    • 60 degrees
    • A right angle
    • Always acute

  3. What does the perpendicular from the centre of a circle to a chord do?

    • Bisects the chord
    • Is a tangent to the circle
    • Is parallel to the chord
    • Doubles the length of the chord

  4. What is the relationship between the radius and the tangent at a point of contact on a circle?

    • They are parallel
    • They coincide
    • They are equal in length
    • They are perpendicular

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

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

  6. Find the centre and radius of x^2 + y^2 - 4x + 6y - 12 = 0.

    • Centre (2, -3), radius 5
    • Centre (-2, 3), radius 5
    • Centre (2, -3), radius sqrt(12)
    • Centre (2, 3), radius 5

  7. What is the equation of the circle with diameter from (0, 0) to (6, 8)?

    • (x + 3)^2 + (y + 4)^2 = 25
    • (x - 3)^2 + (y - 4)^2 = 5
    • (x - 6)^2 + (y - 8)^2 = 25
    • (x - 3)^2 + (y - 4)^2 = 25

  8. The circle x^2 + y^2 = 25 has a point (3, 4). What is the equation of the tangent at (3, 4)?

    • 3x - 4y = -7
    • x + y = 7
    • 3x + 4y = 25
    • 4x + 3y = 25

  9. What are the centre and radius of x^2 + y^2 + 6x - 2y = 6?

    • Centre (3, -1), radius 4
    • Centre (-3, 1), radius 16
    • Centre (-3, 1), radius 4
    • Centre (-3, 1), radius sqrt(6)

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

    • (4, 2)
    • (4, 1)
    • (3, 4)
    • (0, 0)

  11. A circle has centre (1, 2) and radius 5. Where does it meet the x-axis?

    • x = 1 +/- 5
    • x = 1 +/- sqrt(29)
    • x = 1 +/- sqrt(21)
    • x = 2 +/- sqrt(21)

  12. A circle has centre (1, 2) and passes through (4, 6). What is the gradient of the tangent at (4, 6)?

    • 3/4
    • 4/3
    • -4/3
    • -3/4

  13. Points (0, 0), (4, 0) and (0, 2) lie on a circle. What is its centre?

    • (2, 0)
    • (2, 1)
    • (4, 2)
    • (1, 2)

  14. What is the length of the chord cut from the circle x^2 + y^2 = 25 by the line x + y = 0?

    • 5 sqrt(2)
    • 25
    • 5
    • 10

  15. The circle has centre (3, 0) and radius 2. Does the line y = 1 meet it?

    • It is a tangent to the circle
    • It passes through the centre
    • It does not meet the circle
    • It cuts the circle at two points

  16. Which point lies outside the circle x^2 + y^2 = 9?

    • (1, 1)
    • (0, -2)
    • (2, 2)
    • (2, 3)

  17. Find the equation of the circle with centre (2, 3) passing through (5, 7).

    • (x - 2)^2 + (y - 3)^2 = 5
    • (x + 2)^2 + (y + 3)^2 = 25
    • (x - 5)^2 + (y - 7)^2 = 25
    • (x - 2)^2 + (y - 3)^2 = 25

  18. Points A(-3, 0), B(3, 0) and P(0, 3) are given. What is the angle APB?

    • 180 degrees
    • 45 degrees
    • 60 degrees
    • 90 degrees

  19. What is the equation of the circle through (0, 0), (2, 0) and (0, 4)?

    • (x + 1)^2 + (y + 2)^2 = 5
    • (x - 1)^2 + (y - 2)^2 = 5
    • (x - 1)^2 + (y - 2)^2 = 4
    • (x - 2)^2 + (y - 4)^2 = 20

  20. For the circle x^2 + y^2 + 2gx + 2fy + c = 0, what is the centre?

    • (-2g, -2f)
    • (g, -f)
    • (g, f)
    • (-g, -f)

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