InterviewSolution
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InterviewSolution
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Find the equation of the lines through the point (3, 2) which make an angle of `45^@`with the line `x-2y=3`. |
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Answer» Let the slope of the required line be m, Then, its equation is `(y-2)/(x-3)=m.......(i)` Given line is `x-2y=3 Rightarrow y=(1)/(2)x-(3)/(2).....(ii)` Clearly, the slope of this line is `(1)/(2)` It is given that the angle between (i) and (ii) is `45^(@)` `therefore |(m-(1)/(2))/(1+(1)/(2)m)|=tan 45^(@)" "["using tan "theta=|(m_(2)-m_(1))/(1+m_(1)m_(2))|]` `Leftrightarrow (2m-1)/(2+m)=1 or (2m-1)/(2+m)=-1 Leftrightarrow m=3 or m=(-1)/(3)` `therefore ` the required equation is `(y-2)/(y-3)=3 or (y-2)/(x-3)=(-1)/(3)` `i.e. 3x-y-7=0 or 3y-9=0` |
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