Algebra II: Circles Flashcards
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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?

<p>outside</p> Signup and view all the answers

What is the general equation of a circle?

<p>not provided</p> Signup and view all the answers

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.

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