Suppose (12, 8) and (4,6) are the endpoints of a diameter of a circle. Which is an equation of the circle?
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A)
(x + 8)2 + (x - 72 - 17
B)
(x - 3)2 + (y - 7)2 - 17
0
(x + 3)2 – (y + 7)2 - 17
D)
(x – 8)2 + (y – 712 - 289

(x-8)² + (y-7)² - 17 = 0 is the equation of the circle.

Step-by-step explanation:

(12,8) and (4,6) are the endpoints of the diameter of a circle.

The equation of the circle is given as,

(x-h)² + (y-k)² = r²

where (h,k) is the center and r is the radius of the circle.

We have the endpoints of the diameter, from that we can find the center using the mid - point formula as,

center = ( (1/2)(x₁ + x₂), (1/2)(y₁+y₂))

           = ( (1/2)(12+4), (1/2)(8+6))

       = ((1/2)(16), (1/2)(14))

        = (8,7)

To find the radius we can use the distance formula as, using the center (8,7) and end point (12,8)

r = √((x₂- x₁)² + (y₂-y₁)²)

  =  √((12- 8)² + (8-7)²)

 = √((4² + 1²)) = √(16+ 1) = √17

Squaring on both sides, we will get,

r² = 17

So the equation of the circle can be written as,

(x-8)² + (y-7)² = 17

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