If p=(-3,-2) and q=(1,6) are the endpoints of the diameter of a circle find the equation of the circle

The equation of the circle   (x +1) )² +(y-(2))² = (2(√5))²

  or

The equation of the circle    x² + 2 x + y² - 4 y  = 15

Step-by-step explanation:

Given points end  Points are p(-3,-2) and q( 1,6)

The distance of two points formula

P Q =

P Q =

P Q =

The diameter 'd' = 2 r

                       2 r = √80

                            =

                           =

                      r =  2√5

Mid-point of two end points

                                              = (-1 ,2)

Mid-point of two end points = center of the circle

                                    (h,k) = (-1 , 2)

The equation of the circle

           (x -h )² +(y-k)² = r²

         (x -(-1) )² +(y-(2))² = (2(√5))²

        x² + 2 x + 1 + y² - 4 y + 4 = 20

         x² + 2 x + y² - 4 y  = 20 -5

          x² + 2 x + y² - 4 y  = 15

Final answer:-

The equation of the circle   (x +1) )² +(y-(2))² = (2(√5))²

  or

The equation of the circle    x² + 2 x + y² - 4 y  = 15

Step-by-step explanation:

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