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If the line y=sqrt(3)+k touches the circ...

If the line `y=sqrt(3)+k` touches the circle `x^2+y^2=16 ,` then find the value of `kdot`

Text Solution

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Given equation of circle,
`x^(2)+y^(2)=16`
`therefore` Radius=4 and centre=(0,0)
Now, perpendicular from (0,0) to line y=`sqrt3`x+k=Radius of the circle
`abs((0-0+k)/sqrt(3+1))=4`
Since the distance from the point (m,n) to the line Ax+By+k=0 is d=`abs((Am+Bn+c)/(A^(2)+B^(2)))`
`rArrpmk/2=4`
`thereforek=pm8`
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