![\[x\text{ }+\text{ }2y\text{ }+\text{ }3\text{ }=\text{ }0\text{ }and\text{ }3x\text{ }+\text{ }4y\text{ }+\text{ }7\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b96a8f73737fa5c96c93aa542bcb785a_l3.png "Rendered by QuickLaTeX.com")
The equation of the straight line passing through the points of intersection of x + 2y + 3 = 0 and 3x + 4y + 7 = 0 is
![\[\begin{array}{*{35}{l}} x\text{ }+\text{ }2y\text{ }+\text{ }3\text{ }+~\lambda \left( 3x\text{ }+\text{ }4y\text{ }+\text{ }7 \right)\text{ }=\text{ }0 \\ \left( 1\text{ }+\text{ }3\lambda \right)x\text{ }+\text{ }\left( 2\text{ }+\text{ }4\lambda \right)y\text{ }+\text{ }3\text{ }+\text{ }7\lambda ~=\text{ }0 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7e8c4cfb02694290aaf8d51ff4017d2f_l3.png "Rendered by QuickLaTeX.com")
The required line is perpendicular to x − y + 9 = 0 or, y = x + 9
Find the equation of a straight line passing through the point of intersection of x + 2y + 3 = 0 and 3x + 4y + 7 = 0 and perpendicular to the straight line x – y + 9 = 0.
Find the equation of a straight line passing through the point of intersection of x + 2y + 3 = 0 and 3x + 4y + 7 = 0 and perpendicular to the straight line x – y + 9 = 0.