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  • If the line y=√3 x+k touches the circlex^2+y^2=16 , then find the value of k.

If the line y=\sqrt{3}x+k touches the circle x2 + y2 = 16, then find the value of k.

Answers (1)

Given line is y=\sqrt{3}x+k  and the circle is 

x2+y2=16   

Centre of the circle is (0,0) and radius is 4.  

Since the line y=\sqrt{3}x+k touches the circle, perpendicular distance from (0,0) to line

 is equal to the radius of the circle.  

\left | \frac{0-0+k}{\sqrt{3+1}} \right |=4

\pm \frac{k}{2}=4

k=±8

Posted by

infoexpert22

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