Equation of a circle

The Maths Habit

A circle has its centre at (0, 0) and a radius of 5. Name some points on the circle.

(5, 0), (0, −5), (3, 4), (−4, 3), …

Origin
The point (0, 0).
Radius
The distance from the centre of a circle to its edge.

(3, 4) is on the circle with centre (0, 0) and radius 5

345(3, 4)

32 + 42 = 9 + 16 = 25 = 52

Any point (x, y) on a circle with centre (0, 0) and radius r

xyr(x, y)

Pythagoras: x2 + y2 = r2

x2 + y2 = r2

Write down the radius.

x2 + y2 = 144

Write down the radius.

x2 + y2 = 20

Write the equation of the circle.

x2 + y2 = radius2
Radius6
Radius236
x2 + y2 =36

Write the equation of the circle.

Radius7
Radius249
x2 + y2 =49

Write the equation of the circle.

x2 + y2 = radius2
Radius6
Radius236
x2 + y2 =36

A circle has centre (0, 0) and diameter 16. Write its equation.

Radius16 ÷ 2 = 8
Radius264
x2 + y2 =64

Is (6, 8) on the circle x2 + y2 = 100?

62 + 82 = 36 + 64 = 100
insideonoutside

Is (5, 5) on the circle x2 + y2 = 49?

52 + 52 =25 + 25 = 50
insideonoutside

Is (6, 8) on the circle x2 + y2 = 100?

62 + 82 = 36 + 64 = 100
insideonoutside

Is (2, 6) on the circle x2 + y2 = 40?

22 + 62 = 4 + 36 = 40
insideonoutside

Equation of a circle worksheet, page 1

Equation of a circle worksheet, page 2

Answer sheet

  1. A circle with centre (0, 0) passes through (2, 7). Write its equation.

    x2 + y2 = 53

  2. Where does the line y = x cross the circle x2 + y2 = 18?

    (3, 3) and (−3, −3)

  1. The circle has centre (0, 0). Write its equation.

    x2 + y2 = 25
    xy−505−505

  2. Is the point (3, 7) inside, on or outside the circle x2 + y2 = 50? Show how you know.

    Outside: 9 + 49 = 58

  3. A circle has centre (0, 0) and passes through (4, −1). Write its equation.

    x2 + y2 = 17
Exit tickets to print