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Angle Bisectors
Combined Equations of Angle Bisectors of Lines
Related Resources
Angle bisector of two lines (the line which bisects the angle between the two lines) is the locus of a point which is equidistant (having equal perpendicular distance) from the two lines.
L1 : A1x + B1y + C1 = 0
L2 : A2x + B2y + C2 = 0
A1x+B1y+C1/√A12 + B12 = + A2x+B2y+C2/√A22 + B22
2. Rule to decide the particular bisector
When both c1 and c2 are of the same sign, evaluate a1a2 + b1b2. If negative, then acute angle bisector is a1x+b1y+c1/√a12+b12 = + a2x+b2y+c2/√a22+b22.
When both c1 and c2 are of the same sign, the equation of the bisector of the angle which contains the origin is a1x+b1y+c1/√a12+b12 = + a2x+b2y+c2/√a22+b22.
Bisectors of the angle containing the point (α, ß) is a1x+b1y+c1/√a12+b12 = +a2x+b2y+c2/√a22+b22 if a1α + b1ß + c1 and a2α + b2ß + c2 have the same sign.
Bisectors of the angle containing the point (α, ß) is a1x+b1y+c1/√a12+b12 = +a2x+b2y+c2/√a22+b22 if a1α + b1ß + c1 and a2α + b2ß + c2 have the opposite sign.
Solution:
Combined equations of the angle bisectors of the lines represented by ax2 + 2hxy +by2 = 0
Illustration:
The lines are perpendicular if a + b = 0 and coincident if h2 = ab.
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