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Q.
Consider the points $A(0,1)$ and $B(2,0)$, and $P$ be a point on the line $4 x+3 y+9=0$. The coordinates of $P$ such that $|P A-P B|$ is maximum are
Straight Lines
Solution:
The equation of $A B$ is
$\frac{x}{2}+\frac{y}{1}=1 $
or $ x+2 y-2=0 $
$|P A-P B| \leq A B$
Thus, $|P A-P B|$ is maximum if the points $A, B$, and $P$ are collinear.
Hence, solving $x+2 y-2=0$ and
$4 x+3 y+9=0$, we get point $P \equiv(-84 / 5,13 / 5)$
