question_answer

Let two points be \[A(1,-1)\] and\[B(0,2)\]. If a point \[P(x',y')\]be such that the area of \[\Delta PAB=5sq.\]units and it lies on the line, \[3x+y-4\lambda =0,\]then a value of \[\lambda \]is    [JEE MAIN Held On 08-01-2020 Morning]

A) 3         

B) 4

C) 1         

D) -3

Correct Answer: A

Solution :

[a] Given \[3x'+y'=4\lambda \] And \[\Rightarrow \left| x'(-3)-y'(1)+1(2) \right|=10\] \[\Rightarrow \left| -4\lambda +2 \right|=10\] \[\Rightarrow 2-4\lambda =+10\,\,\text{or}\,\,2-4\lambda =-10\] \[\Rightarrow \lambda =-\,2\,\,\text{or}\,\lambda =3\]