InterviewSolution
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InterviewSolution
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Find the equation of the line through the intersection of lines `3x +4y=7` and `x-y+2= 0` and whose slope is 5. |
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Answer» The given lines are 3x+4y-7=0 and x-y+2=0 The equation of any line through the point of intersection of the given line is of the form, `(3x+4y-7)+k(x-y+2)=0........(i)` `Rightarrow (3+k)x+4(4-k)y+(2k-7)=0` `Rightarrow (4-k)y-(3+k)y+(9-2k)` `Rightarrow y=(-(3+k))/(4-k)x+((7-2k))/((4-k))` `Rightarrow y=((k+3))/((k-4))x+((7-2k))/((4-2k)` `"Slope of this line is"((k+3))/((k-4))` `therefore (k+3)/(k-4)=5 Rightarrow k+3=5k-20 Rightarrow 4=23 Rightarrow (23)/(4)` `"Substituting k"=(23)/(4)"in (i), we get "` `(3x+4y-7)+(23)/(4)(x-y+2)=0` `Rightarrow 4(3x+4y-7)+23(x-y+2)=0` `Rightarrow 25x-7y+18=0,` which is the required equation. |
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