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Find the condition for two lines a(1)x+b...

Find the condition for two lines `a_(1)x+b_(1)y+c_(1)=0` and `a_(2)x+b_(2)y+c_(2)=0` to be
`(i)` parallel
`(ii)` perpendicular

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AI Generated Solution

To find the conditions for the two lines given by the equations \( a_1x + b_1y + c_1 = 0 \) and \( a_2x + b_2y + c_2 = 0 \) to be parallel and perpendicular, we will use the concept of the slope of a line. ### Step 1: Find the slopes of the lines The slope \( m \) of a line given by the equation \( ax + by + c = 0 \) is given by: \[ m = -\frac{a}{b} \] For the first line \( a_1x + b_1y + c_1 = 0 \), the slope \( m_1 \) is: ...
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