Most Important Selected Qs for JEE AdvancedMathematicsStraight Lines

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

Options

A(7,-5) if | PA - PB | is maximum
B(- 1 5 ,- 1 5 ) if | PA - PB | is maximum
C(7,-5) if |P A-P B| is minimum
D(- 1 5 ,- 1 5 ) if |P A-P B| is minimum

Correct answer

D. (- 1 5 ,- 1 5 ) if |P A-P B| is minimum

Step-by-step solution

P lies on the line 2 x+3 y+1=0 ....(1) |P A-P B| is maximum if P, A, B are collinear. Equation of the line A B is x+y=2 ....(2) P is the point of intersection of (1) and (2) which is (7,-5) Equation of perpendicular bisector of A B is y=x .....(3) For minimum value of | PA - PB |, P is the point of intersection of (1) and (3) which is (- 1 5 ,- 1 5 )

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