Find the equation of the straight line which passe through the intersecting of the lines x + y - 3 = 0 and 2x - y = 0 and is inclined at an angle of 45° with x-axis.
Answers
Answer :
x - y + 1 = 0
Solution :
Here ,
The given linear equations are ;
x + y - 3 = 0 -------(1)
2x - y = 0 --------(2)
Firstly ,
Let's find the point of intersection of the given lines .
Adding eq-(1) and (2) , we get ;
=> x - y - 3 + 2x - y = 0
=> 3x - 3 = 0
=> 3x = 3
=> x = 3/3
=> x = 1
Now ,
Putting x = 1 in eq-(1) , we get ;
=> x + y - 3 = 0
=> 1 + y - 3 = 0
=> y - 2 = 0
=> y = 2
Thus ,
The point of intersection of the given lines is (1 , 2) .
Here ,
We need to find the equation of a line which passes through the point of intersection of the given lines and having the inclination of 45° with the x-axis in +ve direction (anti clockwise direction) .
We know that ,
=> tanϴ = ∆y/∆x
=> tanϴ = (y - y1)/(x - x1) , where ϴ is the inclination with the x-axis in +ve direction and (x1 , y1) is the point through which the line passes .
Thus ,
The required equation of line will be given as ;
=> tan45° = (y - 2)/(x - 1)
=> 1 = (y - 2)/(x - 1)
=> x - 1 = y - 2
=> x - 1 - y + 2 = 0
=> x - y + 1 = 0