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The sum of squares of the abscissas of all the points on the line x + y = 4 that lie at a unit distance from the line 4 x + 3 y - 10 = 0 is

Correct answer

58

Step-by-step solution

Any point on the line x + y = 4 can be taken as x 1 , 4 - x 1 . As it is at a unit distance from the line 4 x + 3 y - 10 = 0 , we get, 4 x 1 + 3 4 - x 1 - 10 4 2 + 3 2 = 1 ⇒ x 1 + 2 = 5 ⇒ x 1 + 2 = ± 5 ⇒ x 1 = 3 or - 7 ∴ Required sum of the squares = 9 + 49 = 58

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