Asked by Marianna
A circle on the Coordinate plane has a diameter with endpoints at (6,8) and (15,8). What are the coordinates of the center of the circle? What is the radius of the circle? Identify the coordinates of another point on the circle. Explain how you found your answer.
Answers
Answered by
Reiny
midpoint of diameter
= ( (6+15)/2 , (8+8)/2)
= ( 21/2 , 8)
equation:
(x-21/2)^2 + (y-8)^2 = r^2
plug in (6,8)
81/4 + 0 = r^2
(x-21/2)^2 + (y-8)^2 = 81/4
any other point?
how about the y-intercept, let x = 0
441/4 + (y-8)^2 = 81/4
y-8 = ±√90 = ±3√10
y = 8 ±√10
so (0, 8+3√10) and (0,8-3√10) are two more points
= ( (6+15)/2 , (8+8)/2)
= ( 21/2 , 8)
equation:
(x-21/2)^2 + (y-8)^2 = r^2
plug in (6,8)
81/4 + 0 = r^2
(x-21/2)^2 + (y-8)^2 = 81/4
any other point?
how about the y-intercept, let x = 0
441/4 + (y-8)^2 = 81/4
y-8 = ±√90 = ±3√10
y = 8 ±√10
so (0, 8+3√10) and (0,8-3√10) are two more points
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