Start with the circle you see below. Then put the circle on the coordinate system.
Finally, label the circle to show the center and a point on the circle. Recall that (h, k) is the center of the circle and (x, y) is a point on the circle. The distance between (h, k) and (x, y) is the length of the radius.
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Distance formula = √ | (x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2} |
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d = √ | (x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2} |
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r = √ | (x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2} |
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r = √ | (x - h)^{2} + (y - k)^{2} |
Write the standard equation of the circle with center (4, -1) and a radius of 6.
The standard form is (x - h)^{2} + (y - k)^{2} = r^{2}
Substitute (4, -1) for (h, k) and 6 for r.
(x - 4)^{2} + [(y - (-1)]^{2} = 6^{2}
Simplify the equation
(x - 4)^{2} + (y + 1)^{2} = 36
Sep 30, 22 04:45 PM