# Find the equation and the area of the circle if the ends of the diameter (18,-13) and (4,-3). Given endpoints of the diameter in a circle are ( 18. -13) and ( 4, -3).

We need to find the equation of the circle.

We will write into the circle standard equation.

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

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Given endpoints of the diameter in a circle are ( 18. -13) and ( 4, -3).

We need to find the equation of the circle.

We will write into the circle standard equation.

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

Given the end points of the diameter, then we know that the midpoint of the diameter is the center of the circle.

==> xm = (xA+xB) /2 = ( 18+4)/2 = 22/2 = 11

==> ym = (yA+yB)/2 = ( -13-3) /2 = -16/2 = -8

Then the center is m(11,-8).

==> Now we will calculate the length of the diameter.

D =  sqrt( 18-4)^2 + ( -13+3)^2

= sqrt( 14^2 + 10^2)

= sqrt(196+100) = sqrt(296) =  17.2

==> r = d/2 = 17.2/2 = 8.6

==> (y+8)^2 + ( x-11)^2 = 74

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