Question 262337
formula for circle is:


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


(h,k) are the center of the circle.


r is the radius of the circle.


end points of your diameter are (-1,-7) and (5,10).


midpoint of that line is given by the equation:


midpoint of line = ({{{(x1+x2)/2}}} , {{{(y1+y1)/2}}})


since (x1,y1) = (-1,-7) and (x2,y2) = (5,10), this becomes:


midpoint of line = ((-1+5)/2),(-7+10)/2)) = (4/2,3/2) = (2,3/2).


formula for your circle should be {{{(x-2)^2 + (y-(3/2))^2 = r^2}}}


end points of the radius are:


(2,3/2) and (5,20)


length of the radius = {{{sqrt((x2-x1)^2 + (y2-y1)^2)}}}


this becomes:


length of the radius = {{{sqrt((5-2)^2 + (10-3/2)^2)}}}


this becomes:


length of the radius = {{{sqrt(3^2 + (17/2)^2)}}}


this becomes:


length of the radius = {{{sqrt (9 + 289/4) = sqrt (36/4 + 289/4) = sqrt(325/4) = sqrt(81.25)}}}.


since {{{r = sqrt(81.25)}}}, this means that {{{r^2 = 81.25}}}


formula for the circle is:


{{{(x-2)^2 + (y-3/2)^2 = 81.25}}}


to graph this equation, we have to solve for y.


solving for y, we get:


{{{y = 3/2}}} +/- {{{sqrt(81.25 - (x-2)^2)}}}


graph of circle looks like this:


{{{graph(600,600,-12,12,-12,12,(3/2) + sqrt(81.25-(x-2)^2),3/2 - sqrt(81.25-(x-2)^2))}}}