Question

if A=6,0 and B= 0,4 and O is the origin,then the locus of p such that triangle pob=2poa

Answer 1

Answer with explanation:

Coordinates of A, B and O are = (6,0), (0,4) and (0,0)

Let coordinate of point P= (x,y)

⇒Area of Δ POB= 2×Area of ΔPOA

$\rightarrow \frac{1}{2}\times\left[\begin{array}{ccc}x&y&1\\0&0&1\\0&4&1\end{array}\right] =2 \times \frac{1}{2} \times \left[\begin{array}{ccc}x&y&1\\0&0&1\\6&0&1\end{array}\right]\\\\x(0-4)+0+0=2 \times[ 0-y(0-6)+0]\\\\\rightarrow -4 x=12 y\\\\\rightarrow x+3 y=0$