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AP EAMCET201824 Apr 2018Morning ShiftMathematicsStraight LinesActual

The vertex A of a triangle lies on the lines x+y=1 and 2 x+3 y=6 . If the orthocentre of the triangle is O ( 3 7 , 22 7 ) , then the equation of O A in the normal form is

Options

  1. Ax +y =7 ; = ⁻¹ 1 7
  2. Bx +y = 13 17 ; = ⁻¹ ( 1 4 )
  3. Cx +y = 13 4 ; = ⁻¹ ( 13 17 )
  4. Dx +y = 13 17 ; = ⁻¹

Correct answer

D. x +y = 13 17 ; = ⁻¹

Step-by-step solution

Vertex A is point of intersection of the lines x+y=1 and 2 x+3 y=6 Point of intersection =(-3,4) So, A(-3,4) and O ( 3 7 , 22 7 ) Equation of line passing through two points aligned y-4 & = ( 22 7 -4 ) 3 7 +3 (x+3) y-4 & =- 6 24 (x+3) x+4 y & =13 aligned Normal form of line x +y =P Where P= 13 17 , = 1 17 , = 4 17 = 4 1 Hence, required equation is x +y = 13 17 ; = ⁻¹(4) .

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