## Question

The equation represents three straight lines passing through the origin such that

### Solution

Two of them are coincident and two of them are perpendicular

We have,

Clearly, two of the three lines represented by the given equation are coincident and two are perpendicular.

#### SIMILAR QUESTIONS

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 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

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

The equation represents three straight lines passing through the origin such that

If the equation represents two pairs of perpendicular lines, then

If one of the lines represented by the equation is a bisector of the angle between the lines*xy* = 0, then λ =