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Q.
The equation of a line through the point $(1,2)$ whose distance from the point $(3,1)$ has the greatest value is
Straight Lines
Solution:
Obviously, the line through $Q$ is at the greatest distance from point $P$ when it is perpendicular to $P Q$. Now, the slope of line $P Q$ is $m_{P Q}$ $=-1 / 2$. Then the slope of perpendicular line passing through $Q$ is
$y-2=2(x-1)$
or $2 x-y=0$
