The equation of a line through the point (1,2) Whose distance from the point (3,1) has the greatest value is

Answers (1)

Solution:   Any line through  (1,2)

                  y-2=m(x-1)        ..........(1)

             Rightarrow      mx-y+2-m=0

            Length of perp. from (3,1)  to Line (1)

                                h=frac2m+1sqrtm^2+1              ............(2)

            Rightarrow             fracmathrmd hmathrmd m=frac2-m(m^2-11)^frac32            ........(3)

             Rightarrow            fracmathrmd hmathrmd m=0  gives   m=2

           Now ,     fracmathrmd hmathrmd m> 0 for m< 2  and   fracmathrmd hmathrmd m< 0 for  m> 2

              Rightarrow     h is maximum for m=2

            Therefore   ,  (1)   becomes   for   y=2x.

         

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