Question

Find the equation of the circle that has a diameter with endpoints located at (-3, 6) and (9, 6).

Answer 1

Answer:
`(x+3)^2+(y-6)^2 = 36\\\\`

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Step-by-step explanation:

If you apply the midpoint formula to the given points, you should find the midpoint is (3,6). This point represents the center of the circle. This means (h,k) = (3,6).

The radius is r = 6 because this is the distance from the center to either given endpoint. Either count out the spaces or use subtraction of the x coordinates. This works because the y coordinates are all the same.

Use those h, k and r values to plug them into the equation below

`(x-h)^2+(y-k)^2 = r^2\\\\(x-(-3))^2+(y-6)^2 = 6^2\\\\(x+3)^2+(y-6)^2 = 36\\\\`

which represents the equation of the circle we're after.

The graph is below.