Loci
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LOCI IN TWO DIMENSIONS Locus is the path of moving point or set of point that satisfies given conditions
•
A Fixed Point If a point P moves such that it is a constant distance from a fixed point O, its locus is a circle with centre O and radius OP Locus of P
O Radius OP P
2. Two Fixed Points If a point P moves such that it is equidistant from 2 fixed points R and S, its locus is the perpendicular bisector of line RS Locus p
R
s
•
A straight line
If a point P moves such that it is always at constant distance from a straight line MN, its locus is two lines that are parallel to MN
a
Locus P M
b
N
Distance a = Distance b
4. Two intersecting lines • If a point P moves such that its
perpendicular distance from two lines, AB and CD is constant, its locus is the angle bisector of angle AQC and angle AQD, where Q is the intersecting point C B
Locus P
Q
A D
Intersection of 2 loci in two dimensions • The intersection of 2 loci in a two
dimensional plane is point or point that satisfy the conditions of 2 loci. X 5cm Locus A
2cm
P
Q Y
Locus B
•
A Fixed Point If a point P moves such that it is a constant distance from a fixed point O, its locus is a circle with centre O and radius OP Locus of P
O Radius OP P
2. Two Fixed Points If a point P moves such that it is equidistant from 2 fixed points R and S, its locus is the perpendicular bisector of line RS Locus p
R
s
•
A straight line
If a point P moves such that it is always at constant distance from a straight line MN, its locus is two lines that are parallel to MN
a
Locus P M
b
N
Distance a = Distance b
4. Two intersecting lines • If a point P moves such that its
perpendicular distance from two lines, AB and CD is constant, its locus is the angle bisector of angle AQC and angle AQD, where Q is the intersecting point C B
Locus P
Q
A D
Intersection of 2 loci in two dimensions • The intersection of 2 loci in a two
dimensional plane is point or point that satisfy the conditions of 2 loci. X 5cm Locus A
2cm
P
Q Y
Locus B
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