Question 785341
the equation of a circle with equation {{{(x-h)^2+ (y-k)^2=r^2}}}


with a diameter that has endpoints  ({{{-5}}},{{{8}}}) and ({{{9}}},{{{4}}})

first find diameter {{{d}}} which is equal to distance between two given points:

*[invoke distance_formula -5, 8, 9, 4]

since {{{d=14.56}}}
now we know that radius is {{{d/2=r= 7.28}}}

now, find coordinates of the center which will be midpoint of diameter:

*[invoke midpoint -5, 8, 9, 4]

as you can see, the midpoint of the segment joining the two points ({{{-5}}},{{{8}}}) and ({{{9}}},{{{4}}}) is ({{{2}}}, {{{6}}}) which means {{{h=2}}} and {{{k=6}}}

so, equation of a circle will be:

{{{(x-2)^2+ (y-6)^2=(7.28)^2}}}

{{{(x-2)^2+ (y-6)^2=53}}}

{{{drawing( 600, 600, -10, 10, -5, 20,circle(2,6,0.1),locate(2,6,C(2,6)),
  grid( 1 ),circle(-5,8,0.1),circle(9,4,0.1),locate(-5,8,p(-5,8)),locate(8.5,4,p(9,4)),
  green( circle( 2, 6,7.28 ) )
)}}}