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up vote 6 down vote favorite 3 Question : Consider the family of lines $a(3x+4y+6)+b(x+y+2)=0$ Find the equation of the line of family situated at the greatest distance from the point P (2,3) Solution : The given equation can be written as $(3x+4y+6)+lambda (x+y+2)=0$ $Rightarrow x(3+lambda)+y(4+lambda)+6+2lambda =0....(1)$ Distance of point P(2,3) from the above line (1) is given by D= $frac{|2(3+lambda)+3(4+lambda)+6+2lambda|}{sqrt{(3+lambda)^2+(4+lambda)^2}}$ $Rightarrow D = frac{(24+7lambda)^2}{(3+lambda)^2+(4+lambda)^2}$ Now how to maximize the aboved distance please suggest. Thanks geometry optimization coordinate-systems share | cite | improve this question