Question 157301
Find the midpoint of the line connecting the two diameter endpoints. 
That'll be the center of the circle.
{{{x[c]=(-8+(-3))/2}}}
{{{x[c]=-(11/2)}}}
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{{{y[c]=(-1+13)/2}}}
{{{y[c]=6}}}
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The area of a circle is,
{{{A[c]=(pi*D^2)/4}}}
The diameter of the circle is the distance between the endpoints.
{{{D^2=(x[1]-x[2])^2+(y[1]-y[2])^2}}}
{{{D^2=(-8-(-3))^2+(-1-13)^2}}}
{{{D^2=(-5)^2+(-14)^2}}}
{{{D^2=25+196}}}
{{{D^2=221}}}
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{{{A[c]=(pi*D^2)/4}}}
{{{A[c]=(pi*221)/4}}}
or approximately,
{{{A[c]=173.6}}}
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{{{drawing( 300, 300, -15, 5, -5, 15,grid( 1 ),circle(-5.5,6,.3),  circle(-5.5,6,7.43),  circle( -8, -1, .3 ),circle( -3, 13, .3 ),green(line( -8, -1, -3, 13)))}}}