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Question

The point(s) on x+y=4 that lie(s) at a unit distance from the line 4x+3y-10=0 is/are:

A
(7, -11)
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B
(-7, 11)
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C
(-3, -1)
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D
(3, 1)
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Solution

The correct option is D (3, 1)
For the line x+y=4,
Let x=t
y=4-t
Let P(t, 4-t) be a point which is at a unit distance from the line 4x+3y-10=0
(4t+3(4t)1042 + 32=1(t+2|=5t+2=±5t=7 or 3Hence, the required points are (7, 11) and (3, 1).

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