Question:
A line passing through the point \(P(2,1)\) meets the coordinate axes in \(A\) and \(B\). If \(P\) divides \(AB\) in the ratio \(4:3\), then the equation of \(AB\) is
A line passing through the point \(P(2,1)\) meets the coordinate axes in \(A\) and \(B\). If \(P\) divides \(AB\) in the ratio \(4:3\), then the equation of \(AB\) is
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If a line cuts both axes, use intercept form after finding intercepts through section formula.
Updated On: Jul 15, 2026
- \(6x+5y-11=0\)
- \(3x-2y-4=0\)
- \(2x+y-5=0\)
- \(3x+8y-14=0\)
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The Correct Option is D
Solution and Explanation
Let:
\[
A(a,0),\quad B(0,b)
\]
Point \(P(2,1)\) divides \(AB\) in ratio \(4:3\).
By section formula:
\[
P=\left(\frac{4(0)+3a}{7},\frac{4b+3(0)}7\right)
\]
Equate coordinates:
\[
\frac{3a}{7}=2 \Rightarrow a=\frac{14}{3}
\]
\[
\frac{4b}{7}=1 \Rightarrow b=\frac74
\]
Equation in intercept form:
\[
\frac{x}{a}+\frac{y}{b}=1
\]
Substitute:
\[
\frac{x}{14/3}+\frac{y}{7/4}=1
\]
\[
\frac{3x}{14}+\frac{4y}{7}=1
\]
Multiply by \(14\):
\[
3x+8y=14
\]
\[
3x+8y-14=0
\]
Thus,
\[
\boxed{3x+8y-14=0}
\]
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