Question

A and B are the points (2, 0) and (0, 2) respectively. The coordinates of the point P on the line 2 + 3y + 1 = 0 are

• A. (7, -5) if |PA - PB| is maximum
• B. $(\frac{1}{5},\frac{1}{5})$ if |PA - PB| is maximum
• C. (7, -5) if |PA - PB| is minimum
• D. $(\frac{1}{5},\frac{1}{5})$ if |PA - PB| is minimum

Answer 1

The correct option is A (7, -5) if |PA - PB| is maximum

Given two point $A(2,0)$ and $B(0,2)$

Coordinate of P on the line $2x+3y+1=0,$

when $A(2,0)=(x,y)$

$\Rightarrow 2\times 2+3\times 0+1=0\Rightarrow y=-5$

when B(0,2)=(x,y)

$\Rightarrow 2\times 0+3\times 2+1=0\Rightarrow x=7$

$\therefore$ the points (7,-5)

$|PA-PB|=|49-25|=\left|24\right|ismaximum$

$(7,-5)$ if $|PA-PB|$ is maximum