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Circle Equations Worksheet
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Circle Equations Worksheet
📚 Part 1: Understanding Circle Equations
1. The general form of a circle equation is (x - h)² + (y - k)² = r². What does each variable represent?
h and k are the radius, r is the centre
h and k are the centre coordinates, r is the radius
h and k are points on the circle, r is the diameter
h and k are the diameter, r is the centre
2. Which equation represents a circle with centre (3, -2) and radius 5?
(x + 3)² + (y - 2)² = 25
(x - 3)² + (y + 2)² = 25
(x - 3)² + (y + 2)² = 5
(x + 3)² + (y - 2)² = 5
3. For the circle equation x² + y² = 16, identify the centre and radius:
Centre: ( _____ , _____ )
Radius: _____
4. What is the radius of the circle (x - 1)² + (y + 4)² = 49?
✏️ Part 2: Finding Circle Equations
5. Write the equation of a circle with centre (-2, 5) and radius 8.
6. A circle has centre (0, -3) and passes through the point (4, 0). Find the equation of this circle.
7. Find the equation of a circle with centre (6, -1) that passes through the point (2, 2).
8. The endpoints of a diameter of a circle are A(-1, 3) and B(5, -1). Find the equation of the circle.
Hint: The centre is the midpoint of the diameter.
🎯 Part 3: Problem Solving Applications
9. A circular pond has equation (x - 10)² + (y - 8)² = 36, where distances are measured in metres. A walking path goes from point (4, 8) to point (16, 8). Does this path cross through the pond? Explain your reasoning.
10. A radio tower broadcasts in a circular pattern described by the equation (x - 5)² + (y + 2)² = 100, where x and y represent kilometres.
a) What is the range of the broadcast? _____ km
b) Is a house located at coordinates (12, 4) within the broadcast range? Show your work.
11. Find the equation of the circle that has its centre on the x-axis and passes through points (0, 4) and (6, 0).
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