How do you find the equation of a circle whose diameter endpoints of (5,8) and (5,-4)?

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Answer 1 · 2016-11-26T17:47:34

Please see the explanation.

The standard form for the equation of a circle is:

#(x - h)^2 + (y - k)^2 = r^2#

where #x and y# are any point, #(x,y)#, on the circle, #(h,k)# is the center, and r is the radius.

The center of the circle is halfway between the two endpoints, from #(5, 8)# to #(5, -4)#:

#Delta x = (5 - 5) = 0#
#Delta y = (-4 - 8) = -12#

This means that the center is #-6# in the vertical direction from the starting point, #(5, 8)#, which brings us to the point #(5,2)#.

This, also, tells us that the radius is 6.

We have have all of the information that we need to substitute into the standard form:

#(x - 5)^2 + (y - 2)^2 = 6^2#