The points J(-1,-9) and K(5,1) are endpoints of a diameter of circle S. Which equation represents circle S?

  (x -2)² +(y +4)² = 34

Step-by-step explanation:

The center of the circle is the midpoint of the line segment:

  S = (J +K)/2 = ((-1, -9) +(5, 1))/2 = (4, -8)/2 = (2, -4)

The radius of the circle is the distance between the center and either end point. We want the square of the radius for our formula.

  r² = (5 -2)² +(1 -(-4))² = 9 +25 = 34

The equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

Using the numbers we have found, the equation for circle S is ...

  (x -2)² +(y +4)² = 34

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