Straight Line And Pair Of Straight Lines Ques 1
- Consider the set of all lines $p x+q y+r=0$ such that $3 p+2 q+4 r=0$. Which one of the following statements is true?
(2019 Main, 9 Jan I)
(a) Each line passes through the origin.
(b) The lines are concurrent at the point $\left(\frac{3}{4}, \frac{1}{2}\right)$
(c) The lines are all parallel
(d) The lines are not concurrent
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Answer:
Correct Answer: 1.(b)
Solution: (b) Given, $p x+q y+r=0$ is the equation of line such that $3 p+2 q+4 r=0$
Consider, $ 3 p+2 q+4 r=0 $
$\Rightarrow \quad \frac{3 p}{4}+\frac{2 q}{4}+r=0$
(dividing the equation by 4 )
$ \begin{aligned} & \Rightarrow \quad p\left(\frac{3}{4}\right)+q\left(\frac{1}{2}\right)+r=0 \\ & \Rightarrow \quad \left(\frac{3}{4}, \frac{1}{2}\right) \text { satisfy } p x+q y+r=0 \end{aligned} $
So, the lines always passes through the point $\left(\frac{3}{4}, \frac{1}{2}\right)$.
BETA
