The equation of the pair of lines passing thr | vedclass

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(A) The lines passing through the origin and parallel to the given lines $y = m_1x + c_1$ and $y = m_2x + c_2$ are $y = m_1x$ and $y = m_2x$.These can

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$m_1m_2x^2 - (m_1 + m_2)xy + y^2 = 0$

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(A) The lines passing through the origin and parallel to the given lines $y = m_1x + c_1$ and $y = m_2x + c_2$ are $y = m_1x$ and $y = m_2x$.These can be written as $(y - m_1x) = 0$ and $(y - m_2x) = 0$.The joint equation of these two lines is given by the product $(y - m_1x)(y - m_2x) = 0$.Expanding this,we get $y^2 - m_2xy - m_1xy + m_1m_2x^2 = 0$.Rearranging the terms,we get $m_1m_2x^2 - (m_1 + m_2)xy + y^2 = 0$.

The equation of the pair of lines passing through the origin and parallel to the lines $y = m_1x + c_1$ and $y = m_2x + c_2$ is:

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