Question

Find the equations of the straight lines passing through the point (2, 3) and inclined at π/4 radians to the line 2x + 3y = 5.

Solution

Correct option is

x – 5y + 13 = 0 and 5x + y – 13 = 0

 

Let the line 2x + 3y = 5 make an angle θ with positive x-axis. 

  

Now, 

      

                          

Slope of required lines are  

       

  

                            

and, 

      

                           

∴ Equations of required lines are    

        

i.e.  x – 5y + 13 = 0 and 5x + y – 13 = 0.

SIMILAR QUESTIONS

Q1

If the lines ax + y + 1 = 0, x + by + 1 = 0 and x + y + c = 0 (ab and cbeing distinct and difference from 1) are concurrent, then find the value of

Q2

Find the equation of the straight line passing through the point (2, 1) and through the point of intersecction of the lines x + 2y = 3 and 2x – 3y = 4.

Q3

The family of lines x(a + 2b) + y(+ 3b) = b passes through the point for all values of a and b. Find the point.

Q4

If 3a + 2b + 6c = 0 the family of straight lines ax + by + c = 0 passes through a fixed point. Find the coordinates of fixed point.

Q5

 

Find the equation of the line passing through the point of intersection of the lines

          x + 5y + 7 = 0, 3x + 2y – 5 = 0 and   

1. parallel to the line 7x + 2y – 5 = 0

2. perpendicular to the line 7x + 2y – 5 = 0

Q6

 

Find the equation of straight line which passes through the intersection of the straight lines  

        3x – 4y + 1 = 0 and 5x + y – 1 = 0 

and cuts off equal intercepts from the axes.

Q7

Find the orthocentre of the triangle of the triangle ABC whose angular points are A(1, 2), B(2, 3) and C(4, 3).  

Q8

 

If the orthocentre of the triangle formed by the lines

2x + 3y – 1 = 0, x + 2y – 1 = 0, ax + by – 1 = 0   is at origin, then find (a,b).

Q9

 

Find the equations to the straight lines passing through the point (2, 3) and equally inclined to the lines 3x – 4y – 7 = 0 and

12x – 5y + 6 = 0

Q10

 

Find the equations of angular bisector bisecting the angle containing the origin and not containing the origin of the lines

4x + 3y – 6 = 0 and 5x + 12y + 9 = 0.