You can put this solution on YOUR website! Given:
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Let's start by getting rid of the +4 on the left side. Do that by subtracting 4 from both
sides and you have:
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Next, on the left side of this equation let's group all the terms containing x and all the terms
containing y so that we have:
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Let's complete the square for the contents of each set of parentheses. Do this by taking
half of the coefficient of the first degree term, squaring it, and adding the square in
that set of parentheses. (To counter that you also have to subtract the same amount from
the same side of the equation.)
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In the set of parentheses that contain the x terms, take half of the -6 to get -3. Square
that to get +9. Add +9 inside the parentheses and to counter that subtract 9 on the same side
of the equation. As a result you get:
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Use the same process for the set of parentheses containing the y terms. Take half of the
-4 to get -2 and then square the -2 to get +4. Put +4 in the parentheses and subtract
-4 elsewhere on the same side. This results in:
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Note that we have created perfect squares in each set of parentheses. Expressing the contents
of the parentheses as squares results in:
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Combine the two constants on the left side and you have:
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Get rid of the constant on the left side by adding 13 to both sides. This results in:
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This is now in the standard form of the equation of a circle. The center of the circle can
be found by setting each of the contents of the parentheses equal to zero as follows:
. and solve for x by adding +3 to both sides to get
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then:
. and solve for y by adding +2 to both sides to get
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So the center of the circle is (3, 2).
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The radius of the circle is the square root of the right side of the equation for this
circle. So the radius of this circle is So the radius of the circle is
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Hope this helps you to understand the problem and how you solve problems involving the
equation of a circle.
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