Questions and Answers
What is the center of the equation $(x-h)^2+(y-k)^2=r^2$?
(h,k)
Write the equation of a circle with the center (5,-20) and r=8.
(x-5)^2+(y+20)^2=64
What is the equation for a circle with center (4,-3) and radius 3?
(x-4)^2+(y+3)^2=9
If the equation is greater than the radius, where do you shade?
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What is the general equation of a circle?
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Study Notes
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.
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Description
Test your knowledge of circle equations with these Algebra II flashcards. From identifying the center of a circle to writing equations based on given parameters, this set will prepare you for understanding circle geometry. Challenge yourself to recall definitions and formulas related to circles.
