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BITSAT2017MathematicsStraight LinesActual

Two equal sides of an isosceles triangle are 7 x - y + 3 = 0 and x + y - 3 = 0 and its third side passes through the point ( 1 , - 10 ) . The equation of the third side is

Options

  1. Ax - 3 y = - 31
  2. Bx - 3 y = 31
  3. Cx + 3 y = 31
  4. Dx + 3 y = - 31

Correct answer

B. x - 3 y = 31

Step-by-step solution

The third side is parallel to a bisector of the angle between equal sides. The bisectors are 7 x - y + 3 7 2 + - 1 2 = ± ( x + y - 3 ) 1 2 + 1 2 ⇒ 7 x - y + 3 5 2 = ± ( x + y - 3 ) 2 ⇒ 7 x - y + 3 = ± 5 ( x + y - 3 ) ⇒ 2 x - 6 y + 18 = 0 or 12 x + 4 y - 12 = 0 ⇒ x - 3 y + 9 = 0 or 3 x + y - 3 = 0 Let the third side be x - 3 y = k or 3 x + y = L It passes through ( 1 , - 10 ) . ⇒ k = 31 ,   L = - 7 Hence, required lines are x - 3 y = 31 or 3 x + y = - 7 .

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