Asked by Kate
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.
(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.
Answers
Answered by
Damon
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
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
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