Circle Equations: Standard and General Form

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:

1. Group x terms and y terms separately
2. Move the constant term to the right side of the equation
3. Complete the square for x and y terms separately
4. 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