Understanding the equation of a circle is a fundamental concept in geometry. Circles are a unique shape with specific properties, and being able to write the equation of a circle is a valuable skill. This worksheet will help students practice and reinforce their knowledge of this important topic.
By completing the equation of a circle worksheet, students will have the opportunity to work through various problems and scenarios that involve circles. This will help them develop a deeper understanding of the relationship between the coordinates of a circle’s center and its radius, as well as how to write the equation in standard form.
Equation of a Circle Worksheet
1. Identify the center and radius of the following circles and write the equation in standard form:
a) Center: (2, -3), Radius: 5
b) Center: (-1, 4), Radius: 3
2. Determine if the following points lie inside, outside, or on the circle with the given equation:
a) Equation: (x – 1)^2 + (y + 2)^2 = 16, Point: (3, -2)
b) Equation: (x + 2)^2 + y^2 = 25, Point: (-3, 4)
3. Write the equation of a circle with the following characteristics:
a) Center: (5, 7), Passes through the point (3, 9)
b) Center: (-2, -1), Tangent to the x-axis
4. Solve the following system of equations to find the intersection points of the circles:
a) (x – 3)^2 + (y + 4)^2 = 9, (x + 2)^2 + y^2 = 25
b) (x – 1)^2 + y^2 = 16, (x + 4)^2 + y^2 = 25
Completing this worksheet will help students build confidence in their ability to work with circles and their equations. It will also reinforce their knowledge of key concepts such as the center, radius, and standard form of a circle’s equation.