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# A circle passes through the points (-2,0), (2,0), and (3,2). Find the center of the circle.

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A circle passes through the points (-2,0), (2,0), and (3,2). Find  the center of the circle. Enter your answer as an ordered pair.

Apr 7, 2020

#1
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The center of the circle is (0, 2.25)

Hope it helps!

Apr 7, 2020
#2
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To solve this question, you have to make systems of equations, for each point.

As you probably know, the equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where (x, y) is a point on the circle, and (h, k) the center of the circle, and r is the radius.

Now what you have to do is to plug in the values of x and y, and set them equal to each other since we know that the radius is constant.

First of all, you can easily find out the diameter and the radius of the circle, because you have two points where the y-coordinates are constant, so then finding that you can do |-2 -2| which gives you 4, so now you know that the diameter is 4, and the radius is 2.

From this plugging in (-2, 0) you get,

(-2 - h)^2 + (0 - k)^2 = r^2

(-2 - h)^2 + (0 - k)^2 = 4

I'm sure that after you have the idea from here you can distribute, and make 2 more similar equations, then equate and solve. Comment down, if you need another hint or another part of the solution!!

Good Luck with your Geometry Passion!! :)

:)

Apr 7, 2020