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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)Let the required points on the line x+y+1=0 be (h,k)k=−1−hSince the perpendicular distance of (h,k) from the line 3x+4y+2=0 is 15, |3h+4k+2|√32+42=15⇒|3h+4(−1−h)+2|5=15⇒|3h−4−4h+2|=1⇒|−h−2|=1⇒−h−2=1or−h−2=−1∴h=−3,−1 and correspondingly k=2,0The required points are (−3,2) and (−1,0)

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