GCSE · Circles, arcs & sectors

Equation of a circle (x² + y² = r²)Exam-style questions

Why every point of a circle centred at the origin obeys x² + y² = r² (it is Pythagoras), how to read the radius off an equation and describe the graph fully, how to test whether a point is inside, on or outside, how to find the tangent at a point and where it meets an axis, where a line crosses the circle, and how to sketch the circle after a translation.

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19 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    (a) Write down the equation of the circle with centre OO and radius 99.

    (1 mark)
    (b) A different circle has equation x2+y2=0.25x^2 + y^2 = 0.25

    Write down the radius of this circle.

    (1 mark)
    Level 2 · 2 marksTry it
  2. 2
    A circle has centre (0,0)(0, 0)

    The point (−2,6)(-2, 6) lies on the circle.

    Find an equation of the circle.

    (2 marks)
    Level 2 · 2 marksTry it
  3. 3
    A circle has equation x2+y2=42x^2 + y^2 = 42

    Is the point (5,−4)(5, -4) inside the circle, on the circle or outside the circle?

    Tick one box.

    ☐ Inside the circle

    ☐ On the circle

    ☐ Outside the circle

    Show working to support your answer.

    (2 marks)
    Level 2 · 2 marksTry it
  4. 4
    The point (k,3)(k, 3) lies on the circle x2+y2=34x^2 + y^2 = 34

    kk is negative.

    Find the value of kk.

    (2 marks)
    Level 2 · 2 marksTry it