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The circle 𝑥^2 + 𝑦^2 − 4𝑥 − 16𝑦 + 𝑘 = 0 touches the x-axis. Find k and the coordinates of the point of contact. Find the coordinates of the centre and the radius of the circle.

 Nov 24, 2020
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x^2  + y^2   - 4x  -16y  + k  = 0         complete the square on x and y, subtract k from both sides

 

x^2  -4x  + 4  + y^2 - 16y  + 64   = - k + 4 + 64

 

(x - 2)^2  + ( y - 8)^2  =  68  - k

 

The center  =  (2, 8)

 

The radius  =  8   so    r^2 = 64      so.....k = 4

 

Here's a graph  :  https://www.desmos.com/calculator/6ucox9q4dw

 

 

cool cool cool

 Nov 24, 2020

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