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Question

# The coordinates of a point at unit distance from the lines 3x - 4y + 1 = 0 and 3x + 6y + 1 = 0 are

A

(65,110)

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B

(0,110)

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C

(25,1310)

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D

(85,310)

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Solution

## The correct option is D (−85,310) Let (x, y) be the coordinate of the point. 3x−4y+1√32+42=±1 and 8x+6y+1√82+62=±1 3x - 4y - 4 = 0 . . . (1) 3x - 4y + 6 = 0 . . . (2) 8x + 6y - 9 = 0 . . . (3) 8x + 6y + 11 = 0 . . . (4) Solving (1) and (3) we get (x,y) =(65,−110). (1) and (4) we get (x, y) =(−25,−1310) (2) and (3) we get (x, y) =(0,32) and (2) and (4) we get (x, y) =(−85,310)

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