Let two points be A 1 , - 1 and B 0 , 2 . If a point P x ' ,   y ' be such that the area of ∆ P A B = 5 sq. units and it lies on the line 3 x + y - 4 λ = 0 , then a value of λ is

Question

Let two points be A 1 , - 1 and B 0 , 2 . If a point P x ' , &#160; y ' be such that the area of &#8710; P A B = 5 sq. units and it lies on the line 3 x + y - 4 &#955; = 0 , then a value of &#955; is

Aicharya · Accepted Answer

$\Delta = \frac{1}{2} \begin{vmatrix} 0 & 2 & 1 \ 1 & -1 & 1 \ x' & y' & 1 \end{vmatrix}$ $\Rightarrow -2 \begin{vmatrix} 1 & -x' \end{vmatrix} + \begin{vmatrix} y' & x' \end{vmatrix} = \pm 10$ $\Rightarrow -2 + 2x' + y' + x' = \pm 10$ $\Rightarrow 3x' + y' = 12$ or $3x' + y' = -8$ $(x', y')$ lies on the line $3x + y - 4\lambda = 0$, So, $3x' + y' - 4\lambda = 0$. Solving $i$ and $ii$, we get, $\lambda = 3, -2$

Let two points be A 1 , - 1 and B 0 , 2 . If a point P x ' ,   y ' be such that the area of ∆ P A…

Solution

Let two points be A 1 , - 1 and B 0 , 2 . If a point P x ' , &#160; y ' be such that the area of &#8710; P A…

Solution

Let two points be A 1 , - 1 and B 0 , 2 . If a point P x ' , y ' be such that the area of ∆ P A…