Question

# State true or false.If the line y=√3x+k touches the circle x2+y2=16, then the value of k is ±8.

A
True
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B
False
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Solution

## The correct option is A TrueHere the circle has centre at (0,0) and radius 4.The line touches the circle at a point. So, the distance between this point and the centre is equal to the radius of the circle.The distance is same as the perpendicular distance from the point (x1,y1) to the line ax+by+c=0 is given by :|ax1+by1+c|√a2+b2.4=|0+0+k|√3+1|k|=8k=±8

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