Show that the lines y=-x bisects the angle X'OY

Show that the line y= x bisects angle Xoy.

If a x^3 + b y^3 + c x^2 y + d x y^2 =0 represents three distinct straight lines, such that each line bisects the angle between other two, then which of the following is/are correct

Find the equations of the lines bisecting the angles between the lines 4x-3y+12=0 and 12x+5y=20 .

The lines y = mx bisects the angle between the lines ax^(2) +2hxy +by^(2) = 0 if

Find the equations of the lines bisecting the angles between the following pairs of straight lines writing first the bisector of the angle in which the origin lies : 3x-4y+10=0, 5x-12y-10=0

Find the equations of the lines bisecting the angles between the following pairs of straight lines writing first the bisector of the angle in which the origin lies : 12x-5y+3=0, 4x+3y-2=0 .

Show that the line y =x + sqrt7 touches the hyperbola 9x ^(2) - 16 y ^(2) = 144.

Show that the line x- y +4=0 is tangent to the parabola y^(2)= 16x . Find the point of contact.

If the line y = mx bisects the angle between the lines ax^2 + 2h xy + by^2 = 0 then m is a root of the quadratic equation

P is a point equidistant from two lines l and m intersecting at a point A , Show that A P bisects the angle between them.