If the endpoints of the diameter of a circle are (−6, 6) and (6, −2), what is the standard form equation of the circle? a) x2 + (y + 2)2 = 36 b) x2 + (y + 2)2 = 52 c) x2 + (y − 2)2 = 36 d) x2 + (y − 2)2 = 52

  D)  x² + (y − 2)² = 52

Step-by-step explanation:

The center of the circle is the midpoint of the diameter, so is the average of the end points:

  (h, k) = ((-6, 6) +(6, -2))/2 = (0, 4)/2 = (0, 2)

Then the distance between the center and an end point is the radius. It is found using the distance formula:

  r = √((x2 -x1)² +(y2 -y1)²) = √((-6 -0)² +(6 -2)²) = √(36 +16) = √52

Putting these values into the standard form equation for a circle ...

  (x -h)² +(y -k)² = r²

gives ...

  (x -0)² +(y -2)² = (√52)²

  x² +(y -2)² = 52 . . . . . matches choice D

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