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Discussion Response Post to: Straight lines

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anchit saini (4396)

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$1) \mbox{Point of intersection = } [\frac{ab}{a+b},\frac{ab}{a+b}] \\ \\ \mbox{Let the equation of line be }->y=mx + c \\ \\ \mbox{Now since it passes through} \frac{ab}{a+b},\frac{ab}{a+b} ,\mbox{ we get relation as }-> \\ \\ c = \frac{[1-m]ab}{a+b} \\ \\ Also , A -> \frac{-c}{m}, 0 \\ \\ B -> 0, c \\ \\ Mid-Point -> x=\frac{-c}{2m} , y=\frac{c}{2} \\ \\ \mbox{which implies }m = \frac{-y}{x} \\ \\ Hence -> \\ \\ y=\frac{c}{2}=\frac{[1-m]ab}{2(a+b)}=\frac{[x+y]ab}{2x(a+b)}\\ \\ or ->\\ \\ \mbox{2xy(a+b)=ab(x+y)}$

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