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Consider the points \mathrm{A \equiv(0,1)} and \mathrm{B \equiv(2,0)}. \mathrm{'P'} be a point on the line \mathrm{4 x+3 y+9=0}.Coordinates of the point \mathrm{'P'} such that \mathrm{|P A-P B|} is maximum, is

Option: 1

\left(-\frac{12}{5}, \frac{17}{5}\right)


Option: 2

\left(-\frac{84}{5}, \frac{13}{5}\right)


Option: 3

\left(-\frac{6}{5}, \frac{17}{5}\right)


Option: 4

\left(-\frac{24}{5}, \frac{17}{5}\right)


Answers (1)

best_answer

\mathrm{|A B| \geq|P A-P B|} So \mathrm{P A-P B}  is maximum when \mathrm{P} is collinear with \mathrm{AB}


Equation of \mathrm{A B=y-1=\frac{1}{-2}(x-0)}

\mathrm{\Rightarrow \quad 2 y-2=-x \Rightarrow x+2 y=2}
\mathrm{solve\: with \: 4 x+3 y+9=0}

\mathrm{\therefore \quad P\: is \: \left(-\frac{24}{5}, \frac{17}{5}\right)}

Posted by

rishi.raj

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