3.2.1 Circles and their coordinate geometry Quiz: Pearson Edexcel Maths, Unit 3

The 20 questions

1. What is the standard equation of a circle centred at the origin with radius r?

   • x^2 - y^2 = r^2
   • x + y = r
   • (x - r)^2 + (y - r)^2 = 0
   • x^2 + y^2 = r^2

2. What is the standard equation of a circle centred at (a, b) with radius r?

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

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

   • (-3, 4)
   • (-3, -4)
   • (3, -4)
   • (3, 4)

4. What is the radius of the circle given by (x - 2)^2 + (y - 5)^2 = 49?

   • 14
   • 7
   • 49
   • 24.5

5. Which geometrical property is always true for a tangent to a circle and the radius at the point of contact?

   • Equal length
   • Bisecting
   • Perpendicular
   • Parallel

6. What is the geometric property of the perpendicular bisector of any chord in a circle?

   • Is a tangent
   • Touches the circumference
   • Equals the diameter
   • Passes through centre

7. What angle is always subtended by a diameter at the circumference of a circle?

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

8. What is the expanded form of x^2 + y^2 - 4x + 6y - 3 = 0's x-terms grouped?

   • (x + 2)^2 - 4
   • (x - 4)^2 - 16
   • (x - 2)^2 - 2
   • (x - 2)^2 - 4

9. Find the radius of the circle x^2 + y^2 - 6x + 8y = 0.

   • sqrt(7)
   • 5
   • 10
   • 25

10. Find the centre of the circle x^2 + y^2 + 10x - 2y + 1 = 0.

    • (10, -2)
    • (-10, 2)
    • (-5, 1)
    • (5, -1)

11. Determine if the point (3, 4) lies inside, outside, or on the circle x^2 + y^2 = 25.

    • Outside the circle
    • Inside the circle
    • On the circle
    • Centre of circle

12. Determine if the point (1, 2) lies inside, outside, or on the circle x^2 + y^2 = 9.

    • Inside the circle
    • Outside the circle
    • Origin
    • On the circle

13. Determine if the point (6, 8) lies inside, outside, or on the circle x^2 + y^2 = 81.

    • Inside the circle
    • On the circle
    • Tangent point
    • Outside the circle

14. What is the gradient of the radius joining the origin to the point (3, 4)?

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

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

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

16. How many intersection points exist if a line's perpendicular distance from the circle centre equals its radius?

    • 3
    • 0
    • 1
    • 2

17. How many intersection points exist if a line's perpendicular distance from the circle centre is greater than the radius?

    • 1
    • 2
    • 0
    • Infinitely many

18. What is the length of the diameter for a circle with equation (x + 1)^2 + (y - 3)^2 = 16?

    • 16
    • 4
    • 8
    • 32

19. Find the distance from the origin to the centre of the circle (x - 3)^2 + (y - 4)^2 = 1.

    • 3
    • 4
    • 5
    • 1

20. What is the discriminant value when a line is a tangent to a circle in simultaneous quadratics?

    • Undefined
    • Positive
    • Zero
    • Negative

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