AQA · Mathematics · 8300

GCSE Maths: Algebra: equation of a circle

Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Algebra: equation of a circle (Corbettmaths Video 12), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.

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  1. The general equation of a circle with centre (a, b) and radius r is ?

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    (x − a)² + (y − b)² = r²

  2. What are the coordinates of the centre of the circle with equation (x − 3)² + (y − 2)² = 100?

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    (3, 2)

  3. What is the radius of the circle with equation (x − 1)² + (y + 3)² = 16?

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    4 (the square root of 16)

  4. What are the coordinates of the centre of the circle with equation x² + y² = 225?

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    (0, 0) or the origin

  5. What is the radius of the circle with equation x² + y² = 225?

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    15 (the square root of 225)

  6. How do you check if a point (p, q) lies on a circle with equation (x − a)² + (y − b)² = r²?

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    Substitute p for x and q for y; if the equation is satisfied, the point lies on the circle.

  7. What is the equation of a circle with centre (2, 7) and radius 6?

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    (x − 2)² + (y − 7)² = 36

  8. If a circle has equation x² + y² = 144, what is the length of its diameter?

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    24 (radius is 12, so diameter is 2 × 12 = 24)

  9. What is Roberto's mistake if he writes the equation of a circle with centre (0, 0) and radius 9 as x² + y² = 9?

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    He forgot to square the radius; the correct equation is x² + y² = 81.

  10. What is David's mistake if he writes the equation of a circle with centre (0, 0) and radius 9 as x² − y² = 81?

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    He used subtraction instead of addition; the correct equation is x² + y² = 81.

  11. If AB is a diameter of a circle and A is (0, 7) and B is (0, −7), what are the coordinates of the centre?

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    (0, 0)

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