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AP EAMCET202018 Sep 2020Morning ShiftMathematicsStraight LinesActual

Given that lines (L₁: y=m_a x, L₂: y=m_b x ) and (L₃: y=m_c x ) make equal intercepts on the line (x+y=1 ), then

Options

  1. A(2 (1+m_a ) (1+m_ c )= (1+m_b ) (1+m_ b ) )
  2. B(2 (1+m_a ) (1+m_t )= (1+m_b ) (2+m_a+m_t ) )
  3. C( (1+m_a ) (1+m_b )= (2+m_t ) (1+m_a+m_t ) )
  4. D( (1+m_a ) (1+m_b )= (1+m_b ) (2+m_a+m_c ) )

Correct answer

B. (2 (1+m_a ) (1+m_t )= (1+m_b ) (2+m_a+m_t ) )

Step-by-step solution

Since, the point of intersecting of given lines (L₁: y=m_a x, L₂: y=m_b x ) and (L₃: y=m_c x ) with line (x+y=1 ) are ( aligned & A ( 1 1+m_a , m a 1+m_a ), B ( 1 1+m_b , m_b 1+m_b ) and & C ( 1 1+m_c , m_c 1+m_c ) respectively. aligned ) It is given that, (A B=B C A B^2=B C^2 ) ( gathered ( 1 1+m_a - 1 1+m_b )^2+ ( m_a 1+m_a - m_b 1+m_b )^2 = ( 1 1+m_b - 1 1+m_c )^2+ ( m_b 1+m_b - m_c 1+m_c )^2 (m_b-m_a )^2 (1+m_a )^2 (1+m_b )^2 + (m_a-m_b )^2 (1+m_a )^2 (1+m_b )^2 = (m_c-m_b )^2 (1+m_b )^2 (1+m_c )^2 + (m_b-m_c )

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