A16 Equation of a circle and tangents to circles Quiz: AQA Maths, Unit 2

The 20 questions

1. (H) What is the radius of the circle x^2 + y^2 = 81?

   • 81
   • 40.5
   • 9
   • 18

2. (H) What is the equation of a circle with centre at the origin and radius 5?

   • x^2 + y^2 = 5
   • x^2 + y^2 = 25
   • x^2 + y^2 = 10
   • x + y = 25

3. (H) Does the point (3, 4) lie on the circle x^2 + y^2 = 25?

   • No, since 9 + 16 = 24
   • Yes, since 3 + 4 = 25
   • No, since 3 x 4 = 25
   • Yes, since 9 + 16 = 25

4. (H) What is the radius of the circle x^2 + y^2 = 49?

   • 49
   • 2401
   • 24.5
   • 7

5. (H) What is the equation of the circle with centre (0, 0) and radius 3?

   • x^2 + y^2 = 9
   • x^2 - y^2 = 9
   • x^2 + y^2 = 3
   • x + y = 9

6. (H) A tangent to a circle at a point is perpendicular to which line?

   • The radius through that point
   • A chord through that point
   • The arc at that point
   • A second tangent at that point

7. (H) What is the gradient of the radius from the centre (0, 0) to the point (3, 4)?

   • 7
   • -3/4
   • 4/3
   • 3/4

8. (H) What is the gradient of the tangent to x^2 + y^2 = 25 at (3, 4)?

   • -3/4
   • 3/4
   • 4/3
   • -4/3

9. (H) What is the equation of the tangent to x^2 + y^2 = 25 at (3, 4)?

   • 3x + 4y = 25
   • 4x + 3y = 25
   • 3x - 4y = 25
   • 3x + 4y = 12

10. (H) What is the radius of the circle x^2 + y^2 = 10?

    • 10, the value of r squared
    • 5, half of the value 10
    • 100, the square of 10
    • The square root of 10

11. (H) Which point lies on the circle x^2 + y^2 = 100?

    • (5, 5)
    • (6, 8)
    • (8, 8)
    • (6, 7)

12. (H) Is the point (2, 2) inside or outside the circle x^2 + y^2 = 25?

    • Outside, since 2 x 2 = 4 is less than 25
    • Outside, since 2 + 2 = 4 is less than 25
    • On the circle, since 2 + 2 = 4
    • Inside, since 4 + 4 = 8 is less than 25

13. (H) A circle with centre (0, 0) passes through (0, -6). What is its equation?

    • x^2 + y^2 = 36
    • x^2 + y^2 = 6
    • x^2 + y^2 = -36
    • x + y = 36

14. (H) What is the equation of the tangent to x^2 + y^2 = 25 at (5, 0)?

    • y = 5
    • x = 5
    • x = 0
    • y = 0

15. (H) What is the equation of the tangent to x^2 + y^2 = 25 at (0, 5)?

    • y = 5
    • y = 0
    • x = -5
    • x = 5

16. (H) Which point lies on the circle x^2 + y^2 = 13?

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

17. (H) What is the diameter of the circle x^2 + y^2 = 16?

    • 16
    • 4
    • 8
    • 32

18. (H) Which is the equation of a circle with centre (0, 0) and radius 1?

    • x^2 + y^2 = 2
    • x^2 - y^2 = 1
    • x + y = 1
    • x^2 + y^2 = 1

19. (H) What is the gradient of the tangent to x^2 + y^2 = 25 at (-3, 4)?

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

20. (H) How many points does the line y = 5 meet the circle x^2 + y^2 = 25?

    • One point, as it is a tangent
    • Two points, as it is a chord
    • Zero points, since it is outside
    • Three points, since it crosses at the centre

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