This math topic involves practicing how to derive the standard equation of a circle from a given radius. Each problem presents a circle's radius and asks to identify the correct circle equation from two choices. The equations are presented in the standard form \((x-h)^2 + (y-k)^2 = r^2\), where \(r\) is the radius of the circle, and \((h, k)\) represents the coordinates of the circle’s center. The topic focuses on understanding and applying the relationship between a circle's radius and its equation in a coordinate plane.

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Graphing Circles - Radius to Equation Worksheet

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Graphing Circles - Radius to Equation
1
A LaTex expression showing r=4
Which equation would have this radius?
a A LaTex expression showing (x+2) to the power of 2 + (y) to the power of 2 = 4 to the power of 2
b A LaTex expression showing (x-2) to the power of 2 + (y) to the power of 2 = 4 to the power of 2
2
A LaTex expression showing r=2
Which equation would have this radius?
a A LaTex expression showing (x-1) to the power of 2 + (y-3) to the power of 2 = 2 to the power of 2
b A LaTex expression showing (x-1) to the power of 2 + (y-3) to the power of 2 = 7 to the power of 2
3
A LaTex expression showing r=1
Which equation would have this radius?
a A LaTex expression showing (x+1) to the power of 2 + (y+4) to the power of 2 = 1 to the power of 2
b A LaTex expression showing (x+1) to the power of 2 + (y-4) to the power of 2 = 1 to the power of 2
4
A LaTex expression showing r=5
Which equation would have this radius?
a A LaTex expression showing (x) to the power of 2 + (y-3) to the power of 2 = 5 to the power of 2
b A LaTex expression showing (x) to the power of 2 + (y-3) to the power of 2 = 2 to the power of 2
5
A LaTex expression showing r=3
Which equation would have this radius?
a A LaTex expression showing (x+3) to the power of 2 + (y+5) to the power of 2 = 3 to the power of 2
b A LaTex expression showing (x-3) to the power of 2 + (y+5) to the power of 2 = 3 to the power of 2