Question 444943
a)To determine the equation of the circle we need the center and radius. Since its center is given  (2, 3), we calculate the radius:

{{{r=sqrt((-3-2)^2+(-3-2)^2)=sqrt(169)=13}}}. Now we write the equation of the 

circle centered at (2, 3) and passes through (-3, -9):

{{{(x-2)^2+(y-3)^2=169}}}.

b)Since we know the endpoints of diameter the center will be:

{{{X=(2+2)/2=2}}} and {{{Y=(5+13)/2=9}}} the point (2, 9)

To find the radius we find the half of diameter:

{{{r=d/2=(sqrt((2-2)^2+(13-5)^2))/2=4}}} and the equation will be:

{{{(X-2)^2+(Y-9)^2=16}}}