Question

If the pair of lines  lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of the another sector, then      

Solution

Correct option is

 

Given equation is a homogeneous equation of second degree. So, lines represented by it intersect at the origin. Consequently, centre of the circle is at the origin. It is given that the lines represented by the given equation divide the circle into four sectors such that the area of one of the sectors is thrice that of the other. Let θ be the acute angle between the lines. Then, 3θ is the obtuse angle and so  

        

 

   

SIMILAR QUESTIONS

Q1

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    

Q2

 

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.  

        

     

Q3

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   

Q4

 

If the pair of lines  have exactly one line in common, then a =

Q5

If one of the given by , then cequals

Q6

Area of the triangle formed by the line x + y = 3 and angle bisectors of the pair of the straight lines  is 

Q7

 

If the The Pair of Straight Lines given by   forms an equilateral triangle with the line ax + by + c = 0, then (A + 3B)(3A + B) = 

Q8

 

The area (in square units) of the quadrilateral formed by two pair of the lines  

Q9

The equation  represets

Q10

If the equation of the The Pair of Straight Lines passing through (1, 1), one making an angle θ with the positive direction of x-axis and the other making the same angle with the positive direction of y-axis is , then sin 2θ =