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JEE Main202126 Aug 2021Morning ShiftMathematicsStraight LinesActual

Let A B C be a triangle with A ( - 3 , 1 ) and ∠ A C B = θ , 0 < θ < π 2 . If the equation of the median through B is 2 x + y - 3 = 0 and the equation of angle bisector of C is 7 x - 4 y - 1 = 0 , then tan θ is equal to:

Options

  1. A3 4
  2. B4 3
  3. C2
  4. D1 2

Correct answer

B. 4 3

Step-by-step solution

Let, x - coordinate of the point C is α , So coordinate of the point C α , 7 α - 1 4 ∵ ( C  lies on  7 x - 4 y - 1 = 0 ) Hence, mid point of A C is m α - 3 2 , 7 α + 3 8 As, point m lies on the line 2 x + y - 3 = 0 , Substituting, we get α = 3 . So. C ( 3 , 5 ) Hence, slope of AC is 2 3 and slope of 7 x - 4 y - 1 = 0 is 7 4 ∴ tan θ 2 = 7 4 - 2 3 1 + 7 4 × 2 3 = 1 2 ⇒ tan θ = 2 · 1 2 1 - 1 4 = 4 3 ⇒ tan θ = 4 3

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