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

Answer 1

Answer: (D)

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

Intercept form of equation of line is given by:

$\frac{x}{a}+\frac{y}{b}=1$, where a is x-intercept and b is y-intercept

Now, we are given that $b=2a$

$\Rightarrow$ equation of line is given by $2x+y=2a$

Distance of this line from origin is 1 units.

Applying the formulae for distance of a point from a line, and equating it to 1, we get

$|\frac{-2a}{\sqrt{2^2+1^2}}|=1$

$\Rightarrow$$2a=+\sqrt{5}$and $-\sqrt{5}$