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

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

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 
answer your question?

- Doctor Douglas, The Math Forum   

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 

I hope that answers your question.

- Doctor Douglas, The Math Forum   
Associated Topics:
High School About Math
High School Coordinate Plane Geometry
High School Geometry
Middle School About Math
Middle School Geometry

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