Discussion Forum



1)

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


A) $2x+3y=\pm \sqrt{5}$

B) $x+y= \pm 2$

C) $x+y=\pm 2$

D) $2x+y= \pm \sqrt{5}$

Answer:

Option D

Explanation:

Let equation of line be 

 $\frac{x}{a}+\frac{y}{2a}=1$

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$\Rightarrow$ =2x+y=2a

Distance from origin is 

$|\frac{2a}{\sqrt{(2)^{2}+(1)^{2}}}|=|\frac{2a}{\sqrt{5}}|$

$\Rightarrow$   $|\frac{2a}{\sqrt{5}}|=1$

$\Rightarrow$$2a=\pm \sqrt{5}$

 Hence , equation of line is $2x+y= \pm  \sqrt{5}$