Straight Lines
Straight Line
star_batch_jee_advanced_2025
Grade 11
Question:
A straight line through the origin $O$ meets the parallel lines $3x - 4y = 6$ and $6x - 8y + c = 0$ at points $Q$ and $P$ respectively such that $\left|\frac{OP}{OQ}\right| = \frac{4}{3}$. If $c = 2k$, then $k$ is equal to ______.
Step-by-Step Solution
Key Concept: The intercept theorem states that parallel lines divide transversals proportionally.
Using the property of similar triangles or intercept theorem, we have $\frac{OQ}{OP} = \frac{OM}{ON} = \frac{6/5}{|c|/10} = \frac{3}{4}$. This gives $|c| = 16$, so $c = \pm 16$, yielding $k = 4$.
Correct Answer: 4