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JEE Main20199 Apr 2019Morning ShiftMathematicsStraight LinesActual

Slope of a line passing through P ( 2 , 3 ) and intersecting the line x + y = 7 at a distance of 4 units from P , is

Options

  1. A7 - 1 7 + 1
  2. B1 – 7 1 + 7
  3. C5 - 1 5 + 1
  4. D1 – 5 1 + 5

Correct answer

B. 1 – 7 1 + 7

Step-by-step solution

Given, the point P 2 ,   3 on the line x + y = 7 . Let, the point of intersection of the two lines be Q Then, Q can be taken as Q ≡ ( α ,   7 - α ) Given, P Q = 4 units and the distance between the points x 1 ,   y 1   &   x 2 ,   y 2 is x 1 - x 2 2 + y 1 - y 2 2 ⇒ ( α - 2 ) 2 + 7 - α - 3 2 = 4 ⇒ ( α - 2 ) 2 + 4 - α 2 = 4 ⇒ ( α - 2 ) 2 + 4 - α 2 = 4 2 ⇒ α 2 - 4 α + 4 + 16 - 8 α + α 2 = 16 &#86

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