## Question

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

### Solution

Let be the lines represented by the given equation. Then,

and,

Let be perpendicular lines. Then,

Thus, the third line is *y* = *m*_{3}*x* i.e. *y* = *x*.

#### SIMILAR QUESTIONS

The three lines whose combined equation is *y*^{3} – 4*x*^{2}*y* = 0 form a triangle which is

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 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