Question

The straight line passing through the point of intersection of the straight lines$x-3y+1=0$ and $2x+5y-9=0$ and having infinite Slope and at a distance of $2$ units from the origin, has the equation

• A. $x=2$
• B. $3x+y–1=0$
• C. $y=1$
• D. None of these

Answer 1

The correct option is A

$x=2$

Explanation for the correct option:

Given $x–3y+1=0..\left(i\right)$

$2x+5y–9=0..\left(ii\right)$

Multiply $\left(i\right)$ by $2$

$\Rightarrow 2x–6y+2=0..\left(iii\right)$

Subtract $\left(ii\right)$ from it and solve.

$$\begin{gathered} \Rightarrow 2x-6y+2-(2x+5y-9)=0 \\ \Rightarrow 2x-6y+2-2x-5y+9=0 \\ \Rightarrow -11y+11=0 \\ \Rightarrow y=1 \end{gathered}$$

For value of $x$ put value of $y$ in $\left(iii\right)$

$$\begin{gathered} \Rightarrow 2x-6+2=0 \\ \Rightarrow 2x-4=0 \\ \Rightarrow 2x=4 \\ \Rightarrow x=2 \end{gathered}$$

We get values of $x=2$ and $y=1$ which are coordinates of the point of intersection of the straight lines$x-3y+1=0$ and $2x+5y-9=0$ from where the straight line is passing

Given that the line passing through $(2,1)$ has an infinite slope,

So the line will be parallel to the $y$-axis which means the equation of line will be in terms of $x.$

The equation of the line will be $x=2$

Hence the correct option is option A.