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Let k be a positive real number. The line x+y = k and the circle x^2+y^2=k are drawn. Find k so that the line is tangent to the circle.

 Apr 7, 2020
 #1
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By symmetry, the line and the circle are tangent when k = 1.

 Apr 7, 2020
 #2
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That is incorrect, when k=1, the line and circle intersect meaning the line is NOT tangent to the circle.

 

https://www.desmos.com/calculator/l7wp8s7tst

 Apr 7, 2020
edited by HELPMEEEEEEEEEEEEE  Apr 7, 2020
 #3
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The line and circle are tangent when k= 2.

 

Graph

 

Hope it helps!

 Apr 7, 2020
 #4
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thanks

Guest Apr 7, 2020

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