Does anyone know how to solve this??

(x - 3)² + (y + 1)² = 65

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

The centre C is at the midpoint of the endpoints of the diameter.

Using the midpoint formula to find C

C = ( , ) = ( , ) = (3, - 1 )

The radius is the distance from the centre to either of the endpoints of the diameter.

Using the distance formula to find r

with C (3, - 1 ) and (7, 6 ) , then

r =

  =

  =

  =

Then equation of circle is

(x - 3)² + (y - (- 1) )² = ( )², that is

(x - 3)² + (y + 1)² = 65 ← equation of circle

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step-by-step explanation: