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Circle Equations Worksheet

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Circle Equations Worksheet

Use the form (x − a)² + (y − b)² = r², where the centre is (a, b) and the radius is r. Show your working for questions that involve finding a radius or centre.

Read and interpret

A circle equation gives a circle's centre and radius. Look carefully at the signs inside the brackets.

1.In the equation (x − a)² + (y − b)² = r², what do a, b and r represent?

2.A circular signal zone is described by (x − 3)² + (y + 2)² = 25. Select its centre and radius.

Centre (3, −2), radius 5
Centre (−3, 2), radius 5
Centre (3, −2), radius 25
Centre (−3, 2), radius 25

3.A circle has equation x² + y² = 49. State its centre and radius.

4.Find the centre and radius of (x + 4)² + (y − 1)² = 36.

Build the equation

Use the centre and radius to write each equation in the form (x − a)² + (y − b)² = r².

5.Write the equation of a circle with centre (−2, 5) and radius 4.

6.A circle has centre (1, −3) and passes through P(5, 0). Find its radius and equation.

7.The endpoints of a circle's diameter are A(−1, 2) and B(5, 2). Find the centre, radius and equation of the circle.

Reason it out

Use distance from the centre to decide whether a point is inside, on or outside a circle.

8.A circular rainforest listening zone has equation (x − 4)² + (y − 1)² = 25, with distances in kilometres. Is a sensor at (7, 5) inside, on or outside the zone? Show how you know.

9.The circle (x + 2)² + (y − 3)² = 16 has centre (−2, 3). Is Q(0, 4) inside, on or outside the circle? Give a distance-based reason.

10.A circle has equation (x − 6)² + (y + 1)² = 9. What is its centre and radius, and does point (6, 2) lie on the circle?