Question:
Point \((a,2a)\), \(a>0\), lies in region between lines \(3x-y-3=0\) and \(6x-y-6=0\). Then \(a\in\)
Point \((a,2a)\), \(a>0\), lies in region between lines \(3x-y-3=0\) and \(6x-y-6=0\). Then \(a\in\)
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For region between lines, always test sign of both equations.
Updated On: Jun 22, 2026
- \((\frac{3}{2},3)\)
- \((1,\frac{3}{2})\)
- \((1,3)\)
- \((\frac{3}{2},4)\) \bigskip
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The Correct Option is B
Solution and Explanation
Concept:
Check position of point between two parallel lines.
Step 1: Substitute point.
Line 1: \[ 3a-2a-3=a-3 \] Line 2: \[ 6a-2a-6=4a-6 \]
Step 2: Between condition.
\[ (a-3)(4a-6)<0 \]
Step 3: Solve inequality.
\[ a\in(1,\frac{3}{2}) \] \[ \boxed{(B)} \]
Step 1: Substitute point.
Line 1: \[ 3a-2a-3=a-3 \] Line 2: \[ 6a-2a-6=4a-6 \]
Step 2: Between condition.
\[ (a-3)(4a-6)<0 \]
Step 3: Solve inequality.
\[ a\in(1,\frac{3}{2}) \] \[ \boxed{(B)} \]
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