The parallelism condition for two straight li | vedclass

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Question

(C) The first line is given by $ax + by + c = 0$. The slope of this line is $m_1 = -\frac{a}{b}$.The second line is given parametrically by $x = \alph

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$a\alpha + b\gamma = 0$

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(C) The first line is given by $ax + by + c = 0$. The slope of this line is $m_1 = -\frac{a}{b}$.The second line is given parametrically by $x = \alpha t + \beta$ and $y = \gamma t + \delta$. The slope of this line is $m_2 = \frac{\gamma}{\alpha}$.For two lines to be parallel,their slopes must be equal,so $m_1 = m_2$.Substituting the slopes,we get $-\frac{a}{b} = \frac{\gamma}{\alpha}$.Cross-multiplying,we get $-a\alpha = b\gamma$,which simplifies to $a\alpha + b\gamma = 0$.

The parallelism condition for two straight lines,one of which is specified by the equation $ax + by + c = 0$ and the other being represented parametrically by $x = \alpha t + \beta$ and $y = \gamma t + \delta$,is given by:

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