Equation of a circle
AQA GCSE Maths revision on Equation of a circle. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 17 practice questions on this topic.
Sample questions (3 of 17)
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Question 1
A student claims that the equation x^2 + y^2 = 25 represents a circle with a diameter of 25. Why is this incorrect?
- A) The radius is the square root of 25, so the diameter is 10.
- B) The diameter is 25 squared, which is 625.
- C) The equation represents a square, not a circle.
- D) The centre of the circle is not at the origin.
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Answer: The radius is the square root of 25, so the diameter is 10.
In the standard form equation x^2 + y^2 = r^2, the constant term represents the square of the radius. Therefore, if r^2 = 25, the radius r must be 5, making the diameter 10.
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Question 2
If a circle has the equation x^2 + y^2 = r^2, what geometric theorem is the foundation for this formula?
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Answer: Pythagoras' theorem
For any point (x, y) on the circle, the horizontal distance x and vertical distance y form a right-angled triangle with the radius as the hypotenuse. According to Pythagoras' theorem, x^2 + y^2 = r^2.
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Question 3
Which transformation describes the change from x^2 + y^2 = 9 to (x-2)^2 + y^2 = 9?
- A) A translation 2 units to the left.
- B) A translation 2 units to the right.
- C) A translation 2 units upwards.
- D) A reflection in the y-axis.
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Answer: A translation 2 units to the right.
When an equation is written in the form (x - h)^2 + (y - k)^2 = r^2, the centre of the circle is at (h, k). Replacing x with (x - 2) moves the centre from (0, 0) to (2, 0), which is a shift to the right.
Want to test yourself on the remaining cards for this topic?
14 more questions on Equation of a circle — plus mistakes tracking and spaced repetition across the whole Maths spec.