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AP EAMCET202018 Sep 2020Evening ShiftMathematicsStraight LinesActual

A straight line (L₁ ) passing through (A(3,1) ) meets the coordinate axes at (P ) and (Q ) such that its distance from the origin (O ) is maximum. Then area of ( O P Q ) is sq. units

Options

  1. A( 100 3 )
  2. B( 25 3 )
  3. C( 50 3 )
  4. D( 200 3 )

Correct answer

C. ( 50 3 )

Step-by-step solution

(A=(3,1) ) Let slope of line be (m ) ( array ll & y-y₁=m (x-x₁ ) [be the required line] & y-1=m(x-3) array ) ( aligned & y-1=m x-3 m & m x-y+(1-3 m)=0 (i) aligned ) The greatest distance of line from origin passes through (A(3,1) ) is perpendicular to the given line. ( O A P Q ) Slope of (O A ) Slope of ( PQ =-1 ) ( 1 3 m=-1 m=-3 ) Put, (m=-3 ) in Eq. (i), ( aligned -3 x-y+(1-3)(-3) & =0 -3 x-y+(10) & =0 3 x+y+10 & =0 aligned ) ( ) Area of ( P O Q= 1 2 | c^2 a b |= 1 2 | 100 3 1 |= 50 3 sq ) units. Hence, option (c

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