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BITSAT2010MathematicsParabolaActual

If the equations of the pairs of opposite sides of a parallelogram are (x^2-5 x+6=0 ) and (y^2-6 y+5=0 ), then equations of its diagonals are

Options

  1. A(x+4 y=13, y=4 x-7 )
  2. B(4 x+y=13,4 y=x-7 )
  3. C(4 x+y=13, y=4 x-7 )
  4. D(y-4 x=13, y+4 x=7 )

Correct answer

C. (4 x+y=13, y=4 x-7 )

Step-by-step solution

Equations of the sides of the parallelogram are ((x-3)(x-2)=0 ) and ((y-5)(y-1)=0 ) i.e. (x=3, x=2 ; y=5, y=1 ) Hence its vertices are : ( A (2,1) ; B (3,1) ); ( C (3,5) ; D (2,5) ) Equation of the diagonal ( AC ) is (y-1= 4 1 (x-2) y=4 x-7 ) Equation of the diagonal ( BD ) is (y-1= 4 -1 (x-3) 4 x+y=13 )

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