Find the equation of the line parallel to y -axis and drawn through the point of intersection of the lines x – 7 y + 5 = 0 and 3 x + y = 0.
The lines are x − 7 y + 5 = 0 and 3 x + y = 0 .
The equation of any line parallel to y axis and making an intercept of a is given by,
x = a .
The point of intersection of the two lines is obtained by solving the two equations.
x − 7 y + 5 = 0 3 x + y = 0 y = − 3 x (1)
Solve the equation x − 7 y + 5 = 0 using values of y from equation (1).
x − 7 ( − 3 x ) + 5 = 0 x + 21 x + 5 = 0 22 x = − 5 x = − 5 22
Substitute the value of x in equation (1).
y = − 3 × − 5 22 = 15 22
The point of intersection of the line is ( − 5 22 , 15 22 )
The line parallel to y axis is passing through the point of intersection.
a = − 5 22
Thus, the equation of line is x = − 5 22 .
The lines are
The equation of any line parallel to
The point of intersection of the two lines is obtained by solving the two equations.
Solve the equation
Substitute the value of
The point of intersection of the line is
The line parallel to
Thus, the equation of line is
