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Which of the following is the equation for a circle with a diameter that has endpoints at (2, 10) and (10,6)?
A.(x + 6)2 + (y + 8)2 = 80
B.(x - 6)2 + (y - 3)2 = 80
C.(x + 6)2 + (y + 8)2 = 20
D(x - 6)2 + (y - 3)2 = 20

Sagot :

mhanifa

Answer:

  • (x - 6)² + (y - 8)² = 20

Step-by-step explanation:

Find the center, the midpoint of the ends of the diameter.

Use midpoint formula for each coordinate:

  • x = (2 + 10) / 2 = 12/2 = 6
  • y = (10 + 6) / 2 = 16/2 = 8

Find the square of the radius using distance formula between points:

  • (2, 10) and (6, 8)
  • [tex]r^2=(x_2-x_1)^2+(y_2-y_1)^2[/tex]
  • [tex]r^2=(6-2)^2+(8-10)^2[/tex]
  • [tex]r^2=4^2+(-2)^2=16+4 = 20[/tex]

Use the equation of circle:

  • (x - h)² + (y - k)² = r²

We know that (h, k) is the center (6, 8), substitute into above equation:

  • (x - 6)² + (y - 8)² = 20

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