Okay so I won't tell you the situation but I will tell you that it involves a giant swing in my back yard. don't worry about the distance that the swing is from the ground and all that stuff, because it's irrelevant; I already have all the information done right... okay so there's a circle and the bottom off the circle is where the swing lays at rest and that point is ofcourse (0 feet,0 feet) I swung the swing forward and it came to point (11 feet,2.875 feet ). you know those two points are true on this circle, now I need to know the radius of the circle? what is the radius
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Assuming the center of the circle is at (0 , r)
x^2 + (y - r)^2 = r^2
11^2 + (2.875 - r)^2 = r^2
121 + 8.265625 - 5.75r + r^2 = r^2
129.265625 - 5.75r = 0
129.265625 = 5.75r
r = 129.265625 / 5.75
r = 22.480978260869565217391304347826
x^2 + (y - r)^2 = r^2
11^2 + (2.875 - r)^2 = r^2
121 + 8.265625 - 5.75r + r^2 = r^2
129.265625 - 5.75r = 0
129.265625 = 5.75r
r = 129.265625 / 5.75
r = 22.480978260869565217391304347826
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the equation for a circle:
(x - a)² + (y - b)² = r²
your question is not stated very well, but if you're using (0,0) as the bottom of the circle, the value for b will be r (the radius of the circle). the circle will still be centered about the y-axis, so the value for a will be zero. plug these values in along with your point values, and solve for r:
x² + (y - r)² = r²
x² + y² - 2ry + r² = r²
x²/y + y = 2r
r = x²/2y + y/2
r = (11²)/(2*2.875) + 2.875/2
r = 22.5 ft
(x - a)² + (y - b)² = r²
your question is not stated very well, but if you're using (0,0) as the bottom of the circle, the value for b will be r (the radius of the circle). the circle will still be centered about the y-axis, so the value for a will be zero. plug these values in along with your point values, and solve for r:
x² + (y - r)² = r²
x² + y² - 2ry + r² = r²
x²/y + y = 2r
r = x²/2y + y/2
r = (11²)/(2*2.875) + 2.875/2
r = 22.5 ft