Question

 

Find the angle between the lines

                                                                     

where a > b > 0.

Solution

Correct option is

 

The given equation of lines can be written as  

       

and,

       

Comparing the given lines (i) and (ii) with the lines 

         

respectively. We get   

        

and,  

      

Let θ be the acute angle between the lines, then  

     

     

               

               

               

.

 

SIMILAR QUESTIONS

Q1

The vertices of a triangle are A(10, 4), B(–4, 9) and C(–2, –1). Find the equation of the altitude through A.

Q2

Find the equations of the medians of a triangle, the coordinates of whose vertices are (–1, 6), (–3, –9) and (5, –8).

Q3

Find the ratio in which the line segment joining the points (2, 3) and (4, 5) is divided by the line joining (6, 8) and (–3, –2).

Q4

Find the equation of the line through (2, 3) so that the segment of the line intercepted between the axes is bisected at this point.

Q5

 

Find the equation to the straight line which passes through the points (3, 4) and having intercepts on the axes: 

1. equal in magnitude but opposite in sign 

2. such that their sum is 14

Q6

Find the equation of the straight line through the point P(ab) parallel to the lines . Also find the intercepts made by it on the axes.

Q7

The length of perpendicular from the origin to a line is 9 and the line makes an angle of 120o with the positive direction of y-axis. Find the equation of the line.

Q8

Find the equation of the straight line on which the perpendicular from origin makes an angle of 30o with x-axis and which forms a triangle of area  sq. units with the coordinates axes.

Q9

Find the measure of the angle of intersection of the lines whose equations are 3x + 4y + 7 = 0 and 4x – 3y + 5 = 0.

Q10

The slope of a straight line through A(3, 2) is 3/4. Find the coordinates of the points on the line that are 5 units away from A