The equation of a line though the point (1, 2) whose distance from the point (3, 1) has the greatest value is

• Correct answer
  A

  y = 2 x
• B

  y = x + 1
• C

  x + 2 y = 5
• D

  y = 3x − 1

Solution

We have plotted the diagram based on the given information. $\begin{aligned} & \because A B \perp C D \\ & \quad \quad m_{A B} \cdot m_{C D}=-1\end{aligned}$
$\begin{aligned} m_{A B} \cdot\left(\frac{1-2}{3-1}\right) & =-1 \\ m_{A B} & =2\end{aligned}$ $\therefore$ Equation of line $A B$ passing through $(1,2)$ is y − 2 = 2(x − 1) $\Rightarrow \quad y=2 x$

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