Q95 / 150 · MHT CET 2023 (11 May Shift 1) · Mathematics

$\mathrm{a}$ 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
    $x+3 y=10$
  • Correct answer
    B
    $3 x+y=6$
  • C
    $x-3 y+8=0$
  • D
    $3 x-2 y+3=0$

Solution

Let the equation of the line be $$ \frac{x}{\mathrm{a}}+\frac{y}{\mathrm{~b}}=1 $$ This line passes through the point $(1,3)$ $$ \begin{aligned} \therefore \quad & \frac{1}{a}+\frac{3}{b}=1 \\ & \Rightarrow b+3 a=a b \\ & \Rightarrow 2 b=a b \\ & \Rightarrow a=2 \\ \therefore \quad & b=3 a=6 \end{aligned} $$ Equation (i) becomes, $$ \begin{aligned} & \frac{x}{2}+\frac{y}{6}=1 \\ & 3 x+y=6 \end{aligned} $$

Hence, the correct answer is option: 'B'.

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