Algebra II: Circles Flashcards

Circle Equation Basics

• Standard form of a circle's equation is ((x-h)^2+(y-k)^2=r^2) where ((h,k)) is the center and (r) is the radius.
• The center of the circle can be directly identified as ((h, k)).

Example of Circle Equation

• For a circle with center ((5, -20)) and radius (r=8), the equation becomes ((x-5)^2+(y+20)^2=64).

Specific Circle Example

• For a circle centered at ((4, -3)) with a radius of (3), the equation is written as ((x-4)^2+(y+3)^2=9).

Graphical Interpretation

• If the equation of a circle is greater than the radius, the area outside the circle should be shaded, indicating values that lie outside the radius.

Equation Components

• The elements used in the equation are crucial: ((h, k)) denotes the center, while (r^2) denotes the square of the radius, essential for graphing and identifying circle properties.