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I'm having trouble understanding a certain question, so I am asking for an explanation of it. The question is asked in a different language, so my translation will probably be mistake-ridden, I hope you guys can overlook the mistakes (and of course correct them):

Show that for each $ a $ the circle $ (x-a)^2 + (y-a)^2 = a^2 $ touches the axes.

This is literally how the question is formulated, I'm sure that it isn't a hard question so if one of you can explain what they mean by this question I would appreciate it!

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2 Answers 2

The equation $$(x-a)^2 + (y-a)^2 = a^2$$ defines a circle in the plane. The question just asks you to prove that circle touches the coordinate axes of the plane.

(Hint for the question: Where is the center of the circle defined by that equation, and what is its radius?)

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The radius is $ a^2 $ and the center is at $ (a,a) $ , is that the answer already? If so, wow, than that is easy (and unclearly formulated) –  IamPuzzled Sep 13 '12 at 22:24
    
That's not the radius. –  anonymous Sep 13 '12 at 22:29
    
I meant the radius is also $a$ –  IamPuzzled Sep 13 '12 at 22:29
    
Well, that's not quite an answer - you need to indicate why having a center at $(a,a)$ and radius $a$ makes the circle touch the axes. But it's the first step in the (short) journey. –  Neal Sep 13 '12 at 22:35

A slightly different take on your question would be to realize that if your circle touches the $Y$ axis, it must do so at a point $(0, y)$. Substitute $x=0$ in the equation of your circle; can you find a value for $y$? The answer for touching the $X$ axis can be found in a similar way.

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