## Question

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

### Solution

They are equally inclined to one another

Let *y* = *mx* be one of the lines represented by the given equation. Then, *y*= *mx* satisfies it.

Hence the given equation represents three lines passing through the origin such that they are equally inclined with one another.

#### SIMILAR QUESTIONS

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 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

If the equation represents two pairs of perpendicular lines, then