Question 1174553
Find the equation of a circle that has a diameter with the endpoints given by the points A ({{{-5}}},{{{4}}}) and ({{{7}}},{{{9}}})

the length of  a diameter is equal to distance between given points:

*[invoke formula_distance -5, 4, 7, 9] 

{{{d=13}}} => radius is {{{r=13/2}}}

the center of a circle is half way between given points

C ({{{(-5+7)/2}}},{{{(4+9)/2}}})
C ({{{1}}},{{{13/2}}}) => {{{h=1}}} and {{{k=13/2}}}

the equation of a circle is:

{{{(x-h)^2+(y-k)^2=r^2}}}

{{{(x-1)^2+(y-13/2)^2=(13/2)^2}}}

{{{x^2 - 2 x + 1+y^2 - 13 y + 169/4=169/4}}}

{{{x^2 - 2 x + 1+y^2 - 13 y + 169/4-169/4=0}}}

{{{x^2 - 2 x + y^2 - 13 y + 1 = 0}}}


{{{drawing ( 600, 600, -15, 15, -15, 15,
circle(-5,4,.12),circle(7,9,.12),circle(1,13/2,.12),
locate(-5,4,p(-5,4)),locate(7,9,p(7,9)),locate(1,13/2,C(1,13/2)),
graph( 600, 600, -15, 15, -15, 15,(1/2)(13-sqrt(-4x^2+8x+165)),(1/2) (sqrt(-4x^2+8x+165)+ 13))) }}}