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A circle Gamma is tangent to the line y = -2 and also externally tangential to the circle x^2 + y^2 = 1. Given that the center of Gamma is O = (16,a), what is the value of a?

 Jan 16, 2021
 #1
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The center of  the  x^2 + y^2 + 1  =  (0,0)

 

The  radius of  Gamma  =   ( a + 2)  =  r

 

The distance  from (16,a)  to (0, 0) =  (r + 1)  =   ( a + 2 + 1) = (a + 3) 

 

16^2  +  a^2   =  ( a+ 2 + 1)^2

 

256 + a^2  =  (a + 3)^2

 

256  + a^2  =   a^2  + 6a  +  9

 

6a  =  247

 

a = 247/6

 

See the graph here  : https://www.desmos.com/calculator/l9klwgdmus

 

cool coolcool

 Jan 17, 2021

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