Respuesta :

mhanifa

Answer:

  • (x + 3)² + (y - 5)² = 37

Step-by-step explanation:

The center is the midpoint of the diameter, the coordinates are:

  • x(M) = (3 - 9)/2 = -3
  • y(M) = (4 + 6)/2 = 5

The length of the diameter:

  • [tex]d = \sqrt{(-9-3)^2+(6-4)^2} = \sqrt{12^2+2^2} = \sqrt{148} = 2\sqrt{37}[/tex]

The radius is:

  • r = d/2 = [tex]2\sqrt{37} /2 = \sqrt{37}[/tex]

The standard form is:

  • (x - h)² + (y - k)² = r², where (h, k) is the center

Substitute to get:

  • (x - (-3))² + (y - 5)² = (√37)²
  • (x + 3)² + (y - 5)² = 37

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