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AP EAMCET202421 May 2024Morning ShiftMathematicsStraight LinesActual

The area of the triangle formed by the lines represented by 3 x+y+15=0 and 3 x^2+12 x y-13 y^2=0 is

Options

  1. A15 3 2
  2. B15 3
  3. C15 3 4
  4. D15 3

Correct answer

A. 15 3 2

Step-by-step solution

aligned & 3 x+y+15=0 ...(i) & 3 x^2+12 x y-13 y^2=0...(ii) aligned Point of intersection of (2) is (0,0) From (i) and (ii), aligned & x= 9 3 2 , y= 12 3 3 2 & Area = 1 2 [x₁ (y₂-y₃ )+x₂ (y₃-y₁ )+x₃ (y₁-y₂ ) ] aligned Here A (0,0), B ( 9+ 3 2 , 12-2 3 2 ), C ( 9- 3 2 , -12-3 3 2 ) are the vertices of triangle. aligned & = 1 2 [0+ ( 9+ 3 2 ) ( 12-3 3 2 )+ ( 9- 3 2 ) ( -12-3 3 2 ) ] & = 15 3 2 aligned

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