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Determine the solution set using the graphical method x^2+y^2>4 (i) (x-2)^2+y^2<4...

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spock1 | Student, Undergraduate | Honors

Posted September 27, 2011 at 10:36 PM via web

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Determine the solution set using the graphical method

x^2+y^2>4 (i)

(x-2)^2+y^2<4 (ii)

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taylormath | High School Teacher | (Level 2) Adjunct Educator

Posted September 28, 2011 at 6:17 AM (Answer #1)

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The graph of `x^2+y^2=4` is a circle with a center at (0,0) and radius 2.  To represent `x^2+y^2>4` the circle will be dashed and the outside of the circle is shaded.

To represent `(x-2)^2+y^2<4` the circle has a center at (2,0) and radius 2.  The circle will be dashed and shaded on the inside.

The solution set is represented by the intersection of the two shadings.  It is the circle on the right, not including where the two circles intersect.

 

I'm unable to graph with shading, but I hope you can see the solution looking like a pac man figure facing left.

 

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