Find the standard form for the equation of a circle xh2yk2r2

Find the standard form for the equation of a circle (xh)2+(yk)2=r2 with a diameter that has endpoints (10,1) and (1,9).

endpoints of diameter = (-10,1) and (1,-9)

the centre of the circle would be the midpoint of the diameter

so applying midpoint formula to find the centre

midpoint = ( x1+x2/2) , (y1+y2/2)

plugging the values we get

centre = ( -9/2 , - 4 )

now radius is the diatance from centre to one of the endpoints

applying distance formula

radius = sqrt 221 / 4 = 7.43

therefore, equation of circle is

( x + 9/2)^2 + ( y + 4)^2 = 7.43^2