Solution 4.1:6a

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Current revision (08:31, 8 October 2008) (edit) (undo)
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If we write the equation as
If we write the equation as
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{{Displayed math||<math>(x-0)^2 + (y-0)^2 = 9</math>}}
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<math>\left( x-0 \right)^{2}+\left( y-0 \right)^{2}=9</math>
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we can interpret the left-hand side as the square of the distance between the points (''x'',''y'') and (0,0). The whole equation says that the distance from a point (''x'',''y'') to the origin should be constant and equal to <math>\sqrt{9}=3\,</math>, which describes a circle with its centre at the origin and radius 3.
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we can interpret the left-hand side as the square of the distance between the points
 
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<math>\left( x \right.,\left. y \right)</math>
 
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and
 
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<math>\left( 0 \right.,\left. 0 \right)</math>.
 
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The whole equation says that the distance from a point (
 
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<math>\left( x \right.,\left. y \right)</math>
 
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to the origin should be constant and equal to
 
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<math>\sqrt{9}=3</math>, which describes a circle with its centre at the origin and radius
 
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<math>\text{3}</math>.
 
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{{NAVCONTENT_START}}
 
<center> [[Image:4_1_6_a.gif]] </center>
<center> [[Image:4_1_6_a.gif]] </center>
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{{NAVCONTENT_STOP}}
 

Current revision

If we write the equation as

\displaystyle (x-0)^2 + (y-0)^2 = 9

we can interpret the left-hand side as the square of the distance between the points (x,y) and (0,0). The whole equation says that the distance from a point (x,y) to the origin should be constant and equal to \displaystyle \sqrt{9}=3\,, which describes a circle with its centre at the origin and radius 3.


Image:4_1_6_a.gif