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One of the diameter of circle x^2 + y^2 - 2x - 6y + 6 = 0 is a chord to the circle with...
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You may find the radius of the circle using the following formula:
chord length = `2sqrt(r^2 - d^2)`
r expresses the radius of circle
d expresses the perpendicular distance from the center of circle to the chord
You need to find the chord length, hence, you should convert the given equation of the circle into standard form such that:
`(x-h)^2 + (y-k)^2 = r^2`
You should complete the squares such that:
`x^2 + y^2 - 2x - 6y + 6 = 0`
`(x^2 - 2x + 1)+ (y^2 - 6y + 9) - 1 - 9 +6 = 0`
`(x-1)^2 + (y-3)^2 = 4`
You need to identify the center and radius of circle that has the equation `x^2 + y^2 - 2x - 6y + 6 = 0` such that:
`C(1,3) and r = 2`
The length of the chord is the length of diameter, hence chord length = 4.
You need to find the perpendicular distance from the center (2,1) of circle to the chord of length 4, such that:
`d = |(2-1)^2 + (1-3)^2 - 4|/(sqrt(1+1))`
`d = 1/sqrt2 = sqrt2/2`
Substituting 4 for chord length and `sqrt2/2` for d yields:
`4 = 2sqrt(r^2 - 1/2)`
You need to raise to square both side to remove the square root such that:
`4 = r^2 - 1/2 =gt r^2 = 4 + 1/2`
`r^2 = 9/2 =gt r =+- sqrt3/2`
`r = sqrt3/2`
Hence, evaluating the radius of circle of center (2,1), under given conditions, yields`r = sqrt3/2.`
Posted by sciencesolve on June 17, 2012 at 8:15 AM (Answer #1)
Posted by shankcool on June 17, 2012 at 3:33 PM (Answer #2)
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