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A circle centered at the origin is tangent to the line 2x - y + 4 = 0. What is the area of the circle?

 Nov 25, 2020
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This boils down to finding  the distance  from  the origin (0,0)  to the line

 

distance  =    l  2(0)  - 1(0)  + 4 l               4

                   ________________   =      ______   =     the radius of the  circle  

                    sqrt  [ 2^2 +1^2  ]               sqrt (5)

 

The area  of the  circle  =    pi (4/ sqrt (5) )^2   =  (16/5)pi units^2

 

Here's a graph  :    https://www.desmos.com/calculator/6d3n0brtjx

 

 

cool cool cool

 Nov 25, 2020

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