Question

$\sqrt{3}x-y=2$ and $\sqrt{6}x-\sqrt{2}y=2$ are lines.

• A. coincident
• B. parallel
• C. intersecting

Answer 1

The correct option is B parallel

Write the two equations in the general form:
$a_{1}x+b_{1}y+c_1=0and$
$a_{2}x+b_{2}y+c_2=0$,
For two lines to be parallel,
$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
For $\sqrt{3}x-y=2;\sqrt{6}x-\sqrt{2}y=2,\frac{a_1}{a_2}=\frac{\sqrt{3}}{\sqrt{6}}=\frac{1}{\sqrt{2}}\frac{b_1}{b_2}=\frac{-1}{-\sqrt{2}}=\frac{1}{\sqrt{2}}\frac{c_1}{c_2}=\frac{-2}{-2}=1$
Hence $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}.$

Hence, they are parallel.