Question

Following equations represent a pair of coincident lines

$\frac{x}{2}+y+\frac{2}{5}=0;4x+8y+\frac{5}{16}=0$

• A. True
• B. False

Answer 1

The correct option is B False

The given pair of equation can be written as

$\frac{x}{2}+y+\frac{2}{5}=0$

$\frac{4}{x}+8y+\frac{5}{16}=0$

Here, $a_1=\frac{1}{2},b_1=1,c_1=\frac{2}{5}$

And $a_2=4,b_2=8,c_2=\frac{5}{16}$

$\therefore \frac{a_1}{a_2}=\frac{\frac{1}{2}}{4}=\frac{1}{8}$ and $\frac{b_1}{b_2}=\frac{1}{8}$ and $\frac{c_1}{c_2}=\frac{\frac{2}{5}}{\frac{5}{6}}=\frac{32}{25}$

Hence, $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

The given equation do not represent a pair of coincident lines.