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Find the standard form for the equation of a circle (x-h)^2+(y-k)^2=r^2 with a diameter that has endpoints (-5,0) and (8,-6).

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1 Answer

Use midpoint theorem to find the center (h, k):
h = (-5+8)/2 = 3/2, and k = (0-6)/2 = -3
 
Find the diameter,
d = sqrt(13^2+6^2) = sqrt(205)
So,
r = d/2 = (1/2)sqrt(205)
 
Answer: (x - 3/2)^2 + (y+3)^2 = 205/4

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