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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 23, 2020
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2x - y + 4  = 0 

 

This boils down to finding  the  distance  between the origin and  this line

 

This is given by

 

l  2(0)  - 0  + 4 l                   4            

_____________    =        ______   =  the radius of the circle  

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

 

 

 

Area  of circle  =    pi * radius^2  =  pi *(4/sqrt(5) )^2 =   (16/5)pi  units^2

 

Here's the graph to show this  :  https://www.desmos.com/calculator/xlkqr2a40h

 

 

cool cool cool

 Nov 24, 2020

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