Straight Lines
Family of Lines
JEE Main 2019
Grade 11
Question:
Consider the set of all lines $px + qy + r = 0$ such that $3p + 2q + 4r = 0$. Which is true?
(1) Lines are concurrent at $(3/4, 1/2)$
(2) Lines all pass through origin
(3) Lines have $y$-intercept $= -3/2$
(4) No two of these lines are parallel
Step-by-Step Solution
Key Concept: The condition $3p + 2q + 4r = 0$ can be written as $r = -(3p + 2q)/4$. Substitute into $px + qy + r = 0$ and factor to find the fixed point.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)