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Questions and Answers
Which of the following is the distance from the center of the circle to any point on the circle?
Which of the following is the distance from the center of the circle to any point on the circle?
- Radius (correct)
- Chord
- Tangent line
- Diameter
What is the standard form of the equation of a circle whose center is at (h, k)?
What is the standard form of the equation of a circle whose center is at (h, k)?
- $(x-h)^2 + (y-k)^2 = r^2$ (correct)
- $(x-h)^2 - (y-k)^2 = r^2$
- $x^2 + y^2 = r^2$
- $(x+h)^2 + (y+k)^2 = r^2$
Which of the following statements is NOT true of the radius?
Which of the following statements is NOT true of the radius?
- $\sqrt{(x-h)^2 + (y-k)^2} = r$
- $x^2 + y^2 = r^2$
- $4 + 4 = r$ (correct)
- $(x-h)^2 - (y-k)^2 = r$
What is the standard form of the equation of the circle with the equation $x^2 + y^2 - 4x - 2y - 4 = 0$?
What is the standard form of the equation of the circle with the equation $x^2 + y^2 - 4x - 2y - 4 = 0$?
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What are the coordinates of the center of the circle with the equation $x^2 + y^2 - 4x - 2y - 4 = 0$?
What are the coordinates of the center of the circle with the equation $x^2 + y^2 - 4x - 2y - 4 = 0$?
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Study Notes
Circle Properties and Equations
- The distance from the center of a circle to any point on the circle is called the radius.
- The standard form of the equation of a circle centered at (h, k) is (x - h)² + (y - k)² = r², where r represents the radius.
Radius Statements
- A statement that is NOT true of the radius may often refer to properties or definitions not applicable to circles, such as claims regarding diameters or other shapes.
Conversion to Standard Form
- To convert the equation $x^2 + y^2 - 4x - 2y - 4 = 0$ to standard form, complete the square for both x and y variables.
Center Coordinates
- For the circle represented by the equation $x^2 + y^2 - 4x - 2y - 4 = 0$, the center coordinates can be determined by rearranging the equation after completing the square, yielding center coordinates of (2, 1).
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