Locus – Review
Page 10
In 1-6, describe fully the following loci. Points that are:
1. equidistant from two parallel lines.
The locus of points is a line parallel to the given lines
midway between them.
2. equidistant from two points.
The locus of points is the perpendicular bisector of the
segment formed by joining the points.
3. equidistant from two intersecting lines.
The locus of points is a pair of lines that bisect the angles
formed by the intersecting lines.
4. At a given distance d from a line.
The locus of points is a pair of lines, parallel to original line
on either sides at a distance d from the line.
5. At a given distance d from the point (3,1)
The locus of points is a circle centered at (3,1) with a radius of d.
In 7-15, write an equation for each locus.
7. Points in which the abscissa is 3 less than the ordinate.
x  y 3
8. Points on a line parallel to the x-axis that passes through
the point (7,-1)
y  1
9. Points 8 units from the y-axis.
x  8 and x  8
10. Points 8 units from the origin.
x 2  y 2  64
11. Points equidistant from A(3,2) and B(3,6)
y4
In 7-15, write an equation for each locus.
12. Points equidistant from A(3,2) and B(-9,2)
x  3
13. Points equidistant from the two lines x=7 and x=13
x  10
14. Points 3 units from the fixed point (2,6).
x  22   y  62  9
a) Center : (0,0)
Radius : 4
b) Center : (0,0)
Radius : 6
c) Center : (5,0)
Radius : 10
d) Center : ( 1,9) Radius : 10
12 units to the
1) 12  16 2  17 2
1  256  289
257  289
2) (-8)2  152  17 2
64  225  289
289  289
x2
3 cm
p
3 cm
3 cm
q
A
23.How many points are 3 units from AB and 4 units from B?
(1) 1
(2) 2
(3) 3
(4) 4
3
A
3
4
B
24.The number of points equidistant from two parallel lines and also
equidistant from two points on one of the lines is
(1) 1
(2) 2
(3) 3
(4) 4