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NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

Point P - 1,7 lies on the line 4 x + 3 y = 17 . Then the coordinates of the points farthest from the line which are at a distance of 10 units from the point P are

Options

  1. A7,13 and - 9,1
  2. B5,15 and - 1 , - 7
  3. C- 1,5 and 15 , - 7
  4. D15,5 and - 7 , - 1

Correct answer

A. 7,13 and - 9,1

Step-by-step solution

There are two points A & B which are at a distance of 10 units from P and farthest ( 10 unit distance) from the line 4 x + 3 y = 17 . The slope of A B = 3 4 Because the slope of 4 x + 3 y = 17 is - 4 3 Let line A B makes an angle θ with x -axis then tan ⁡ θ = 3 4 ⇒ cos ⁡ θ , sin ⁡ θ = 4 5 , 3 5 ⇒ A or B = 10 cos ⁡ θ - 1,10 sin ⁡ θ + 7 or ⇒ A or B = - 10 cos ⁡ θ - 1, - 10 sin ⁡ θ + 7 ⇒ A or B = 7,13 or - 9,1

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