## Question

The combined equation of the lines *L*_{1} and *L*_{2} is 2*x*^{2} + 6*xy* + *y*^{2} = 0 and that of the lines *L*_{3} and *L*_{4} is 4*x*^{2} + 18*xy* + *y*^{2 }= 0. If the angle between *L*_{1}and *L*_{4} be α, then the angle between *L*_{2} and *L*_{3} will be

### Solution

We observe that the combined equation of the bisectors of the angles between the lines in the first pair is

and that of the second pair is

Clearly, equations (i) and (ii) are same. Thus, the two pairs of lines have the same bisector. Consequently, they are equally inclined to each other. Hence, the angle between *L*_{2} and *L*_{3} is also α.

#### SIMILAR QUESTIONS

The angle between the pair of lines whose equation is

If two of the straight lines represented by are at right angles, then,

The orthocentre of the triangle formed by the pair of lines and the line *x* + *y* + 1 = 0 is

If the distance of a point (*x*_{1}, *y*_{1}) from each of the two straight lines, which pass through the origin of coordinates, is δ, then the two lines are given by

The equation of two straight lines through the point (*x*_{1}, *y*_{1}) and perpendicular to the lines given by

The equation of the straight lines through the point (*x*_{1}, *y*_{1}) and parallel to the lines given by

The triangle formed by the lines whose combined equation is

The combined equation of the pair of lines through the point (1, 0) and perpendicular to the lines represented by

The equation *x*^{3} + *ax*^{2}*y* + *bxy*^{2} + *y*^{3} = 0 represents three straight lines, two of which are perpendicular, then the equation of the third line is

The lines represented by and the lines represented by are equally inclined then