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Question

# The coordinates of a point on the line x+y+1=0 which is at a distance 15 unit from the line 3x+4y+2=0 are

A
(2,3)
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B
(3,2)
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C
(0,1)
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D
(1,0)
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Solution

## The correct options are B (−3,2) D (−1,0)Any point on the line x+y+1=0, =(−t−1,t) Now, distance of this coordinate from the line 3x+4y+2=0 is given as 15 ∣∣∣3(−1−t)+4t+2√32+42∣∣∣=15 ⇒∣∣∣t−1√25∣∣∣=15 ⇒|t−1|5=15 ⇒|t−1|=1 ⇒t−1=±1⇒t=2 or 0 Thus, putting the values of t in the parametric form of point on the line, we get coordinates as (−3,2) and (−1,0)

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