MHT CET · Maths · Straight Lines
\(\mathrm{a}\) and \(\mathrm{b}\) are the intercepts made by a line on the co-ordinate axes. If \(3 \mathrm{a}=\mathrm{b}\) and the line passes through \((1,3)\), then the equation of the line is
- A \(x+3 y=10\)
- B \(3 x+y=6\)
- C \(x-3 y+8=0\)
- D \(3 x-2 y+3=0\)
Answer & Solution
Correct Answer
(B) \(3 x+y=6\)
Step-by-step Solution
Detailed explanation
Let the equation of the line be
\(\frac{x}{\mathrm{a}}+\frac{y}{\mathrm{~b}}=1\)
This line passes through the point \((1,3)\)
\(\begin{aligned}\therefore & \frac{1}{a}+\frac{3}{b}=1 \\& \Rightarrow b+3 a=a b \\& \Rightarrow 2 b=a b \\& \Rightarrow a=2 \\\therefore \quad & b=3 a=6\end{aligned}\)
Equation (i) becomes,
\(\begin{aligned}& \frac{x}{2}+\frac{y}{6}=1 \\& 3 x+y=6\end{aligned}\)
\(\frac{x}{\mathrm{a}}+\frac{y}{\mathrm{~b}}=1\)
This line passes through the point \((1,3)\)
\(\begin{aligned}\therefore & \frac{1}{a}+\frac{3}{b}=1 \\& \Rightarrow b+3 a=a b \\& \Rightarrow 2 b=a b \\& \Rightarrow a=2 \\\therefore \quad & b=3 a=6\end{aligned}\)
Equation (i) becomes,
\(\begin{aligned}& \frac{x}{2}+\frac{y}{6}=1 \\& 3 x+y=6\end{aligned}\)
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