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Possible bug or I am blind about something??

Posted 11 years ago
Just wanted to plot a circle to solve an analytic geometry problem:  The equation of the circle is (x-2)^2 + (y+1)^2 == 6^2  I had mathematica solve for y so I could plot both sides of the circle.  
Mathematica returned the following results:
{{y->-1-Sqrt[-4+4 x-x^2+36 ^2]},{y->-1+Sqrt[-4+4 x-x^2+36 ^2]}}
When the circle was plotted, the circle had a radius around 38 instead of 6 as indicated in the standard form of a circle.

What am I missing here???
POSTED BY: Raymond Low
6 Replies
Posted 11 years ago
Thankfully rare stumbling block in Mathematica: you can insert invisible operators in equations. I think I managed to find a shortcut for invisible addition (or something similar) once, and scratched my head for half and hour trying to understand what made my results so strange.
POSTED BY: Jari Kirma
Posted 11 years ago
Solve[(x - 2)^2 + (y + 1)^2 == 6^2  , y]
Solve[(x - 2)^2 + (y + 1)^2 == 6^2, y]
Plot[{-1 - Sqrt[-4 + 4 x - x^2 + 36^2], -1 +
   Sqrt[-4 + 4 x - x^2 + 36^2]}, {x, -40, 40}]
Plot[{-1 - Sqrt[32 + 4 x - x^2], -1 + Sqrt[32 + 4 x - x^2]}, {x, -10,
{{y->-1-Sqrt[-4+4 x-x^2+36 ^2]},{y->-1+Sqrt[-4+4 x-x^2+36 ^2]}}
{{y->-1-Sqrt[32+4 x-x^2]},{y->-1+Sqrt[32+4 x-x^2]}}

Thanks Bruce - seems you were right.  I retyped that equation and got the right results.  it seems what I thought were just spaces, were something else.  What can I do to tell what non-printing characters slipped in??   again, thanks all for your help...
POSTED BY: Raymond Low
"What can I do to tell what non-printing characters slipped in?? "

May be this can help how-to-find-pieces-of-code-responsible-for-syntax-errors

It is about hidden chars that can slip in sometimes into the notebook cell.
POSTED BY: Nasser M. Abbasi
There might have been a non-printing character that slipped into the input before the 6^2.
The corresponding output has  36 space ^2, which is suspicious.

You can select the cell bracket and go to Cell menu - Cell Expression.   The problem might be apparent.

Usual fixes are
- re-type that section of the input, or the whole input, and
- select the input, use Edit menu - CopyAs - Plain Text, and paste it into a different place in the notebook.
POSTED BY: Bruce Miller
Are you sure that the results you quote were returned by this Solve command?

Mathematica cannot have returned these solutions because they are not fully evaluated.  Note the 36^2 - 4 part.  Mathematica would always print 1292.

The actual solution returned by version 9.0.1 is correct.
POSTED BY: Szabolcs Horvát
I get this, what do you see?
Plot[y /.  Solve[ (x - 2)^2 + (y + 1) ^2 == 6^2, y], {x, -10, 10},
AspectRatio -> 1, PlotRange -> {{-10, 10}, {-10, 10}}]
POSTED BY: C ormullion
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