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I need help solving this question im hard stuck on it

I Need Help Solving This Question Im Hard Stuck On It class=

Sagot :

Answer:  [tex](\text{x}-1)^2+(\text{y}+6)^2 = 9[/tex]

Explanation

The highest and lowest points on the circle are at (1,-3) and (1,-9) respectively.

Apply the midpoint formula on them to determine the center is at (1,-6). Effectively you are just finding the midpoint of y = -3 and y = -9 to get y = (-3 + -9)/2 = -12/2 = -6. The x coordinate is stuck at x = 1 the entire time.

We determine that h = 1 and k = -6 because the center is located at (h,k)

The distance from (1,-3) to (1,-9) is 6 units. This is the diameter of the circle. Half of which is the radius r = 3.

Plug h = 1, k = -6, r = 3 into the template below to finish up the problem.

[tex](\text{x}-h)^2+(\text{y}-k)^2 = r^2\\\\(\text{x}-1)^2+(\text{y}-(-6))^2 = 3^2\\\\(\text{x}-1)^2+(\text{y}+6)^2 = 9\\\\[/tex]

I used the graphing tool GeoGebra to confirm the answer is correct. Desmos can be used as well.

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