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AP EAMCET202017 Sep 2020Evening ShiftMathematicsStraight LinesActual

The line (x+y=1 ) meets the lines represented by the equation (y^3-6 x y^2+11 x^2 y-6 x^3=0 ) at the points (P, Q, R ). If (O ) is the origin, then ((O P)^2+(O Q)^2+(O R)^2= )

Options

  1. A( 85 72 )
  2. B( 121 72 )
  3. C( 212 72 )
  4. D( 217 72 )

Correct answer

B. ( 121 72 )

Step-by-step solution

We are given with a cubic equation which represents 3-lines. Let lines have, (y-m₁ x=0 ; y-m₂ x=0 ) and (y-m₃ x=0 ) Then, ( (y-m₁ x ) (y-m₂ x ) (y-m₃ x )=0 ) is the combined equations Which in this case is, (y^3-6 x y^2+11 x^2 y-6 x^3=0 ) By comparison we are able to put above equation are, ((y-x)(y-2 x)(y-3 x)=0 ) So, lines are, ( aligned L₁ & y-x=0 L₂ & y-2 x=0 and L₃ & y=3 x=0 aligned ) Their intersection points with ( aligned x+y=1 & are, P & x+y=1 and y-x=0 P & ( 1 2 , 1 2 ) Q & x+y=1 and y-2 x=0 aligned ) ( a

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