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AP EAMCET202418 May 2024Morning ShiftMathematicsStraight LinesActual

The area of the triangle formed by the pair of lines 23 x^2-48 x y+3 y^2=0 with the line 2 x+3 y+5=0 is

Options

  1. A1 13 3
  2. B25 13 3
  3. C7 13 5
  4. D9 25 3

Correct answer

B. 25 13 3

Step-by-step solution

Given the equation 23 x^2-48 x y+3 y^2=0 After solving this equation we get two lines aligned & L ₁: y= ( 24+13 3 3 ) x & ~L ₂: y= ( 24-13 3 3 ) x and L ₃: y= -2 x-5 3 aligned After solving ( L ₁, ~L ₂ ), ( L ₂, ~L ₃ ) and ( L ₁, ~L ₃ ) We get (0,0), ( -5 26-13 3 , 65 3 -120 3(26-13 3 ) ) and ( -5 26+13 3 , -65 3 -120 3(26+13 3 ) ) So, required area = 1 2 | array ccc 0 & 0 & 1 -5 26-13 3 & 65 3 -120 3(26-13 3 ) & 1 -5 26+13 3 & -65 3 -120 3(26+13 3 ) & 1 array | aligned & = 1 2 325 3 +600 3(676-507) + 325 3 -600 3(

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