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Q.

Distance of the origin from the line (1+3)y+(1−3)x=10 along the line y=3x+k is

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a

5/2

b

52+k

c

10

d

0

answer is D.

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Detailed Solution

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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