Question

Let $O\equiv (0,0),A\equiv (0,4),B\equiv (6,0)$. $P$ be a moving point such that the area of $△POA$ is two times the area of $△POB$. Locus of $P$ will be straight line whose equation can be

• A. $x+3y=0$
• B. $x+2y=0$
• C. $2x-3y=0$
• D. $3y-x=0$

Answer 1

Answer: (A), (D)

The correct options are
A $x+3y=0$
D $3y-x=0$

Area of $△OAP=\frac{1}{2}\times OA\times$ height $=\frac{1}{2}\times 4\times |x|$
Area of $△OBP=\frac{1}{2}\times OB\times$ height $=\frac{1}{2}\times 6\times |y|$
Now its given Area of $△OAP=2\times$ Area of $△OBP⟹\frac{1}{2}\times 4\times |x|=2\times \frac{1}{2}\times 6\times |y|$
$⟹|x|=3|y|⟹x=3y$ or $x+3y=0$