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The number of points on the line x + y = 4 which are unit distance apart from the line 2x + 2y = 5 is (A) 0 (B) 1 (C) 2 (D) Infinity

The number of points on the line x + y = 4 which are unit distance apart from the line 2x + 2y = 5 is
(A) 0 (B) 1 (C) 2 (D) Infinity

Grade:

2 Answers

Saurabh Koranglekar
askIITians Faculty 10341 Points
11 months ago
Dear student

The answer is option a \ parallel lines with non unit distance

Regards
Vikas TU
14149 Points
11 months ago

let L: 4x + 3y + C = 0 be a line of unit distance and parallel to the line 4x + 3y = 10

then (C + 10)/sqrt(4^2 + 3^2) = +/- 1

then C = -5 or -15

then L: 4x + 3y - 5 = 0 ---(1)

or 4x + 3y - 15 = 0 ---(2)

the intersecting point of x + y = 4 ---(3)with L is the required point

4(3) - (1), we get y = 11 ==> x = -7 ie the point is (-7, 11)

or 4(3) - (2), we get y = 1 ==> x = 3 ie the point is (3, 1)

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