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The coordinates of the point P on the line $2 x + 3 y + 1 = 0$ , such that $| P A - P B |$ is maximum, where A is (2, 0) and B is (0, 2) is

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(5, –3)

(7, –5)

(9, –7)

(11, –9)

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detailed solution

Correct option is B

|PA−PB|≤|AB| Maximum value of |PA−PB| is |AB| , which is possible only when P, A, B are collinear.If P (x, y) then equation AB is x2+y2=1⇒ x+y=2 ….(i) Now solving Eq. (i) and 2x+3y+1=0 ….(ii)There we get, x=7, y=−5 ∴ P=(7,−5)

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