Question

Two lines represented by the equation  are rotated about the point (1, 0), the line making the bigger angle with the positive direction of the x-axis being turned by 45o in the clockwise sense and the other line being turned by 15o in the anticlockwise sense. The combined equation of the pair of lines kin their new position is    

Solution

Correct option is

 

We have,   

          

  

  

Thus, the lines represented by the given equation are y – + 1 =0 and y +x – 1 = 0.   

these lines intersect at (1, 0). One of them makes 45o angle with x-axis and the other makes 135o angle with x-axis. 

The equations of the new lines are   

     

   

The combined equation of these two lines is    

       

.

SIMILAR QUESTIONS

Q1

 

The square of the distance between the origin and the point of intersection of the lines given by  

           

Q2

The centroid of the triangle whose three sides are given by the combined equation  

Q3

If first degree terms and constant term are to be removed from the equation , then the origin must be shifted at the point

Q4

The angle between the straight lines joining the origin to the points of intersection of  and 3x – 2y = 1 is

Q5

All chords of the curve  which subtend a right angle at the origin always pass through the point

Q6

 

If the pair of lines represented by   intersect on y-axis, then  

Q7

If the chord y = mx + 1 of the circle x2 + y2 = 1 subtends an angle of 45oat the major segment of the circle, then m =

Q8

 

The straight lines represented by

 

Q9

The equation  of the image of the pair of rays  in the line mirror x= 1 is

Q10

 

The value of λ for which the lines joining the point of intersection of curves C1 and C2 to the origin are equally inclined to the axis of X.