Find the equation of the circle, in standard form, where (1, –5) and (–3, 6) are end points of a diameter.

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We know that the equation of the circle into the standard form is:

(x-a)^2 + (y-b)^2 = r^2  where (a,b) is the center is the circle and r is the radius.

Given the points (1,-5) and (-3,6) are the end points of the diameter.

Then the midpoint will be the center of the circle.

==> Mx = (1-3)/2 = -2/2 = -1

==> My = (-5+6)/2 = 1/2

Then the center (a,b) = (-1, 1/2)

==> (x+1)^2 + (y-1/2)^2 = r^2

Now let us calculate the radius.

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