Question

 

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.  

        

     

Solution

Correct option is

 

The combined equation of the straight lines joining the origin to the points of intersection of C1 and C2 is a homogeneous equation and is given by 

        

.   

Lines given by this equation are equally inclined with X-axis. 

∴  Sum of their slopes = 0  

   

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

Q5

 

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

Q6

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 =

Q7

 

The straight lines represented by

 

Q8

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

Q9

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    

Q10

If one of the lines given by the equation  coincide with one of those given by  and the other lines represented by them be perpendicular, then