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 http://mathforum.org/dr.math/ 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). I hope that answers your question. - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/ |
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