## 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

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

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 45^{o} in the clockwise sense and the other line being turned by 15^{o} in the anticlockwise sense. The combined equation of the pair of lines kin their new position is

The value of λ for which the lines joining the point of intersection of curves *C*_{1} and *C*_{2} to the origin are equally inclined to the axis of *X*.

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

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

If one of the given by , then *c*equals

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

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

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

The equation represets

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 =