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Questions and Answers
The ______ form of a circle equation is (x - h)^2 + (y - k)^2 = r^2
standard
The center of a circle is represented by the coordinates (h, ______)
k
To convert a circle equation from general form to ______ form, complete the square for x and y terms separately
standard
To graph a circle, first identify the ______ (h, k) and radius r from the standard form equation
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The ______ formula can be used to find the radius of a circle
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The ______ formula can be used to find the center of a circle
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Study Notes
Circle Equations
Standard Form The standard form of a circle equation is:
(x - h)^2 + (y - k)^2 = r^2
- (h, k) is the center of the circle
- r is the radius of the circle
General Form The general form of a circle equation is:
x^2 + y^2 + dx + ey + f = 0
- This form can be converted to standard form by completing the square
Converting to Standard Form To convert a circle equation from general form to standard form:
- Group x terms and y terms separately
- Move the constant term to the right side of the equation
- Complete the square for x and y terms separately
- Simplify and write in standard form
Graphing Circles To graph a circle, identify the center (h, k) and radius r from the standard form equation.
- Plot the center point (h, k) on the coordinate plane
- Draw a circle with center (h, k) and radius r
Important Properties
- The distance formula can be used to find the radius of a circle
- The midpoint formula can be used to find the center of a circle
Circle Equations
Standard Form
- The standard form of a circle equation is (x - h)^2 + (y - k)^2 = r^2
- (h, k) represents the center of the circle
- r represents the radius of the circle
General Form
- The general form of a circle equation is x^2 + y^2 + dx + ey + f = 0
- This form can be converted to standard form by completing the square
Converting to Standard Form
- To convert from general form to standard form, group x terms and y terms separately
- Move the constant term to the right side of the equation
- Complete the square for x and y terms separately
- Simplify and write in standard form
Graphing Circles
- To graph a circle, identify the center (h, k) and radius r from the standard form equation
- Plot the center point (h, k) on the coordinate plane
- Draw a circle with center (h, k) and radius r
Important Properties
- The distance formula can be used to find the radius of a circle
- The midpoint formula can be used to find the center of a circle
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Description
Learn about the standard and general forms of circle equations, including converting between the two. Understand the role of the center and radius in circle equations.
