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August 12th, 2012, 02:17 PM   #1
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The Radius of a Circle

Given this equation: x^2 + y^2 - 2x - 2y = -9

Is this the equation of a circle? It appears to me that this circle has a negative radius, and this does not make sense to me. The square root of -9 is imaginary, and therefore it seems that this equation cannot graph a circle.
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August 12th, 2012, 04:04 PM   #2
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Re: The Radius of a Circle

Hello, awinston!

Quote:
Given this equation:

Is this the equation of a circle?
It appears to me that this circle has a negative radius, and this does not make sense to me.
The square root of -9 is imaginary, and therefore it seems that this equation cannot graph a circle.

You happen to be correct . . . but for the wrong reason.

The minus on the "9" is not the proper indicator.

We must complete the square first.







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Got it?

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August 12th, 2012, 05:07 PM   #3
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Re: The Radius of a Circle

Yes, of course! Thank you so much.

When I apply this to the problem that I'm actually working on, I see that the circle really does exist.

Andrew
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