A straight line is drawn through a given point `P(1,4)dot`Determine th – InterviewSolution

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1.	A straight line is drawn through a given point `P(1,4)dot`Determine the least value of the sum of the intercepts on thecoordinate axes.
Answer» `y-y_1=m(x-x_1)` `(x_1,y_1)=(1,4)` `y-y_!=m(x-1)` at y intercept,x=0 `y=4-m` at x intercept,y=0 `x-1=-4/m` `x=(m-4)/m` `S=((m-4)/m)+(4-m)` `(dS)/(dm)=(0+4/m^2-1)=0` `4/m^2=1` `m=pm2` `(d^2S)/(dm^2)=-8/m^3` When m=2,`(d^2S)/(dm^2)=-8/8=-1<0` This will be maximum When m=-2,`(d^2S)/(dm^2)=-8/-8=1>0` This will be minimum `x=(m-4)/m=(-2-4)/(-2)=3` `y=4-m=4+2=6` S=3+6=9.

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