Question

The distance between the pair of parallel lines given by $x^2-1005x+2006=0$ is:

• A. $1001$
• B. $1000$
• C. $1005$
• D. $2006$

Answer 1

The correct option is A

$1001$

Solving the given equation:

$$\begin{gathered} x^2-1005x+2006=0 \\ \Rightarrow x^2-1003x-2x+2006=0 \\ \Rightarrow x(x-1003)-2(x-1003)=0 \\ \Rightarrow x=1003\text{or}2 \end{gathered}$$

Drawing the graph of the equation obtained

We have two equations $x=1003\&x=2$

Both the graphs will be parallel to the y-axis.

Hence, the distance between the two parallel lines will be $1003-2=1001$

Therefore, the correct answer is Option (A).