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### Why Use h and k for the Center of a Circle?

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Date: 05/09/2000 at 15:15:25
From: Christine
Subject: Formula

Why are k and h used in the following equation?

(x-h)^2 + (y-k)^2
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```
Date: 05/09/2000 at 16:10:20
From: Doctor Douglas
Subject: Re: Formula

Hi Christine,

You didn't actually write an equation, but I think I can guess what
this is all about. The equation:

(x-h)^2 + (y-k)^2 = r^2

is satisfied by a set of points (x,y), for a given h, k and r. It is a
very special set of points, namely, those (x,y) that lie on a circle
that has radius r and is centered at the point (h,k). For example, the
set of points on the circle of radius 3 that is centered at (-2,4) is:

(x+2)^2 + (y-4)^2 = 3^2

So h and k are the coordinates of the center of the circle. Does that

- Doctor Douglas, The Math Forum
http://mathforum.org/dr.math/
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```
Date: 05/11/2000 at 19:11:29
From: Christine
Subject: formula

In the equation (x-h)^2 + (y-k)^2 why are the variables h and k used?
What is the meaning of the variables h and k?  Why not j and f, etc.?
```

```
Date: 05/12/2000 at 11:48:46
From: Doctor Douglas
Subject: Re: Formula

Hi Christine,

Thanks for writing back. I think the letters h and k are used simply
because they aren't commonly used for other things. For example, f and
g are often used to denote functions, and i and j are used for
counting indices. This leaves h and k for the coordinates of the
center of the circle. To take this one step further, I've seen the
letters (h,k,l) used to refer to the center of a sphere (in
3-dimensions).

- Doctor Douglas, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
High School Coordinate Plane Geometry
High School Geometry