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We have to Find the condition that the diagonals of the parallelogram formed by the lines $ax + by + c = 0$; $ ax + by + c′ = 0$; $a′x + b′y + c = 0$ & $ a′x + b′y + c′ = 0$ are at right angles.

I thought of a method but it is too long . That is first all coordinated then write the equation .

Is there is no other method?

  • 0
    how do we Need four lines to compute this intersection Point of the diagonals? – 2017-01-28
  • 0
    Do u mean the process of finding the gradients of the diagonal is lengthy ? – 2017-01-28

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Hint: The pairs of equation have only constant difference which means pair of equations are parallel. Parallelogram with perpendicular diagonals is always a rhombus. Can you take it from here? Hope it helps.