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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
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B
(15,15) if |PA - PB| is maximum
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C
(7, -5) if |PA - PB| is minimum
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D
(15,15) if |PA - PB| is minimum
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Solution

## The correct option is A (7, -5) if |PA - PB| is maximumGiven 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)⇒2×2+3×0+1=0⇒y=−5when B(0,2)=(x,y)⇒2×0+3×2+1=0⇒x=7∴ the points (7,-5)|PA−PB|=|49−25|=|24|ismaximum(7,−5) if |PA−PB| is maximum

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