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$Distance of the origin from the line (1 + \sqrt{3}) y + (1 - \sqrt{3}) x = 10 along the line y = \sqrt{3} x + k is$

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a

5/2

b

52+k

c

10

d

0

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detailed solution

Correct option is D

The distance from a point P (x1,y1) to a line ax+by+c=0 along a line which makes an angle θ with x - axis then d=ax1+by1+cacosθ+bsinθ The distance from origin to the line (1+3)y+(1−3)x=10 along a line whose inclination is 60∘ d=101-3cos60∘+1+3sin60∘=1012-32+32+32=102=5

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