Question

Consider the set of all lines $px+qy+r=0$ such that $3p+2q+4r=0$. Which of the following statement is true?

• A. The lines are all parallel.
• B. The lines are concurrent at the point $(\frac{3}{4},\frac{1}{2})$.
• C. The lines are not concurrent.
• D. Each line passes through the origin.

Answer 1

The correct option is B The lines are concurrent at the point $(\frac{3}{4},\frac{1}{2})$.

Given, the equation of the set of lines is,
$px+qy+r=0$.............(i)
such that
$3p+2q+4r=0$.............(ii)
Dividing (ii) by 4 and subtrating from (i)
$\Rightarrow (x-\frac{3}{4})p+(y-\frac{1}{2})q=0$
The lines pass through the point $(\frac{3}{4},\frac{1}{2})$.
Hence, the lines are concurrent at the point $(\frac{3}{4},\frac{1}{2})$.