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Pre-Calculus 1st Quarter Exam

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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?

Radius (correct)

Chord

Tangent line

Diameter

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?

$\sqrt{(x-h)^2 + (y-k)^2} = r$

$x^2 + y^2 = r^2$

$4 + 4 = r$ (correct)

$(x-h)^2 - (y-k)^2 = r$

What is the standard form of the equation of the circle with the equation $x^2 + y^2 - 4x - 2y - 4 = 0$?

<p>$(x+2)^2 + (y+1)^2 = 9$</p> Signup and view all the answers

What are the coordinates of the center of the circle with the equation $x^2 + y^2 - 4x - 2y - 4 = 0$?

<p>C:(-2,-1)</p> Signup and view all the answers

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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Description

Pre-Calculus 1st Quarter Examination evaluates your understanding of essential concepts such as the equation of a circle, diameter, radius, and tangent line. Test your knowledge with multiple-choice questions and determine your score.