Question 226045: find the equation of the circle of smallest radius that contains the points (1,4) and (-3,2) within or on its boundary?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! find the equation of the circle of smallest radius that contains the points (1,4) and (-3,2) within or on its boundary?
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The smallest circle thru 2 points will have the 2 points diametrically opposite.
The diameter will be the distance between the points, and the center will be the midpoint.
Midpoint:
find the average of x and y separately
x: (1-3)/2 = -1
y: (4+2)/2 = 3
Center of circle at (-1,3)
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The radius is the distance from the center to either point.
r^2 = diffy^2 + diffx^2
r^2 = 1 + 4 = 5
Standard form for a circle centered at (h,k) with radius r is:
(x-h)^2 + (y-k)^2 = r^2
(x+1)^2 + (y-3)^2 = 5
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