Question

$L_1$ is a line intersecting $x$ and $y$ axis at $P(a,0)$ and $Q(0,b)$. $L_2$ is a line perpendicular to $L_1$intersecting $x$ and $y$ axis at $R$ and $S$ respectively

If the area of the triangle $ORS$ is 4 times the area of the triangle $OPQ$ then equation of $PS$ is

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

Answer 1

Answer: (B), (D)

The correct options are
B $2x+y=2a$
D $2x-y-2a=0$

Area of the $△ORS=\frac{1}{2}ab{k}^2=4\times \frac{1}{2}ab$

$\Rightarrow k^2=4\Rightarrow k=\pm 2$

Equation of $PS$ is $\frac{x}{a}\pm \frac{y}{2a}=1\Rightarrow 2x\pm y=2a$