Question

$A$ straight line makes an intercept on the $Y$-axis twice as long as that on $X$-axis and is at a unit distance from the origin. Then the line is represented by the equations

• A. $ 2\,x + 3\,y = \pm \sqrt{5}$
• B. $ x + y = \pm 2$
• C. $ x - y = \pm 2$
• D. $ 2\,x + y = \pm \sqrt{5}$

Answer 1

Answer: (D)

Let equation of line be
$\frac{x}{a}+\frac{y}{2 a}=1$

$\Rightarrow 2 \,x+y=2\,a$
Distance from origin is
$\left|\frac{2 a}{\sqrt{(2)^{2}+(1)^{2}}}\right|=\left|\frac{2 a}{\sqrt{5}}\right| $
$\Rightarrow \left|\frac{2 a}{\sqrt{5}}\right|=1 $
$\Rightarrow 2 \,a=\pm \sqrt{5}$
Hence, equation of line is $2\, x+y=\pm \sqrt{5}$