average x = (4-4)/2 = 0
average y = (-5 +1)/2 = -2
so center at (0,-2)
half the distance between the two given points
d = diameter = sqrt(8^2 + 6^2) =sqrt(64+36) = sqrt(100 = 10
so radius = 5
(x-k)^2 + (y-h)^2 = r^2
here for center at (0,-2) k=0 and h = -2
x^2 + (y+2)^2 = 25
The points (4, –5) and (– 4, 1) are endpoints of a diameter of a circle.
(a) Find the center of the circle.
(b) Find the length of the radius of the circle. (Note that this is a distance.) Give the exact answer. Show work.
(c) State the equation of the circle (in standard form). Note that you know the center and the radius from the previous parts.
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