SOLUTION: Hi everyone, I was wondering if someone could show me how to find the equation of a circle which has a centrepoint of (-2, 5) and passes through point (1,3). I also need to know wh

Question 200662: Hi everyone, I was wondering if someone could show me how to find the equation of a circle which has a centrepoint of (-2, 5) and passes through point (1,3). I also need to know what the radius of the circle is.
If someone could show me how to do the previous with full working, with steps and notation i would be really grateful.
Thnaks again, -Nick.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
find the equation of a circle which has a centrepoint of (-2, 5) and passes through point (1,3). I also need to know what the radius of the circle is.
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The radius is the distance from the center to the point (1,3), so find that.
r^2 = diffy^2 + diffx^2
r^2 = (5-3)^2 + (-2-1)^2 = 4 + 9
r = sqrt(13)
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The center is offset from the Origin by x = 2 and y = -5
The eqn has the form (x-a)^2 + (y-b)^2 = r^2 where (a,b) is (-2,5)
So it's
(x + 2)^2 + (y-5)^2 = 13
Note that the values are subtracted.
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That can be expanded
x^2 + 4x + 4 + y^2 - 10y + 25 = 13
x^2 + 4x + y^2 - 10y = -16

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