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Show that the lines a(1)x+b(1)y+c(1)=0 a...

Show that the lines `a_(1)x+b_(1)y+c_(1)=0 and a_(2)x+b_(2)y+c_(2)=0,"where" b_(1),b_(2) ne 0 "are (i) parallel, if"(a_(1))/(b_(1))=(a_(2))/(b_(2))" (ii) perpendicular, if "a_(1)a_(2)+b_(1)b_(2)=0`

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To show that the lines \( a_1x + b_1y + c_1 = 0 \) and \( a_2x + b_2y + c_2 = 0 \) are parallel or perpendicular under the given conditions, we will follow these steps: ### Step 1: Understanding the Slope of a Line The general form of a line is given by \( ax + by + c = 0 \). The slope \( m \) of the line can be expressed as: \[ m = -\frac{a}{b} \] where \( a \) is the coefficient of \( x \) and \( b \) is the coefficient of \( y \). ...
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