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COMEDK2024MathematicsStraight LinesActual

For what value of a and b the intercepts cut off on the co-ordinate axes by the line a x-b y+8=0 are equal in length but opposite in signs to those cut off by the line 2 x-3 y+6=0 on the axes

Options

  1. Aa=- 8 3 b=-4
  2. Ba=- 8 3 b=4
  3. Ca= 8 3 b=4
  4. Da= 8 3 b=-4

Correct answer

A. a=- 8 3 b=-4

Step-by-step solution

The equation of the line is 2x - 3y + 6 = 0 . Rewriting in intercept form x A + y B = 1 : 2x - 3y = -6 x -3 + y 2 = 1 . The intercepts are A = -3 and B = 2 . The intercepts of the line ax - by + 8 = 0 are equal in length but opposite in sign to these, so the intercepts are A' = -(-3) = 3 and B' = -(2) = -2 . The equation of the line with intercepts A' and B' is x 3 + y -2 = 1 . Multiplying by 6 gives 2x - 3y = 6 , or 2x - 3y - 6 = 0 . Comparing ax - by + 8 = 0 with the line having intercepts 3 and -2 , we first wri

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