MHT CET · Maths · Straight Lines
The line cuts \(X\) and \(Y\) axes at the points \(A\) and \(B\) respectively. The point \((5,6)\) divides the line segment \(\mathrm{AB}\) internally in the ratio \(3: 1\), then equation of line is
- A \(2 x+y=16\)
- B \(2 x+5 y=40\)
- C \(2 x-y=4\)
- D \(2 x-5 y=-20\)
Answer & Solution
Correct Answer
(B) \(2 x+5 y=40\)
Step-by-step Solution
Detailed explanation
Let \(A \equiv(a, 0)\) and \(B \equiv(0, b)\)
Let \(P \equiv(5,6)\) and it divides \(A B\) in the ratio \(3: 1\)
\(\begin{array}{l}
5=\frac{3 \times 0+1(a)}{3+1} \Rightarrow 5=\frac{a}{4} \Rightarrow a=20 \\
6=\frac{3 b+1 \times 0}{3+1} \Rightarrow 3 b=24 \Rightarrow b=8
\end{array}\)
Thus intercepts on \(X\) and \(Y\) axes are 20 and 8 respectively. Equation of \(\mathrm{AB}\) is \(\frac{\mathrm{x}}{20}+\frac{\mathrm{y}}{8}=1\) i.e. \(2 \mathrm{x}+5 \mathrm{y}=40\)
Let \(P \equiv(5,6)\) and it divides \(A B\) in the ratio \(3: 1\)
\(\begin{array}{l}
5=\frac{3 \times 0+1(a)}{3+1} \Rightarrow 5=\frac{a}{4} \Rightarrow a=20 \\
6=\frac{3 b+1 \times 0}{3+1} \Rightarrow 3 b=24 \Rightarrow b=8
\end{array}\)
Thus intercepts on \(X\) and \(Y\) axes are 20 and 8 respectively. Equation of \(\mathrm{AB}\) is \(\frac{\mathrm{x}}{20}+\frac{\mathrm{y}}{8}=1\) i.e. \(2 \mathrm{x}+5 \mathrm{y}=40\)
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