Name ___________________________ Period __________________________ Geometry
Date _________________________ Mrs. Schuler
Q4 Circle Equation and Locus-Test Review
Part 1: KNOW THE 5 LOCUS!
1. When given a point and a fixed distance from the point the drawing of the locus is:
A circle
2. When given a line and a fixed distance from the line, the drawing of the locus is:
2 parallel lines, also parallel to the given line
3. When given two points, the drawing of the locus of points equidistant from the points is:
A perpendicular bisector of the line connecting the given points
4. When given parallel lines, the locus equidistant from those lines
1 line parallel to the given lines and down the center
5. When given intersecting lines, the locus equidistant from the lines is:
A pair of angle bisectors
Part 2: Multiple Choice and matching column
6.
The term concentric circle means:
a. Two circles side by side
b. Multiple circles with the same center
c. Multiple circles with the same diameter
d. Multiple circles with the same radius
7. The standard equation of a circle with the center at the origin of a coordinate system is:
a. (x-h)2 + (y-k)2 = r2
b. X2 + y2 = r2
c. (x+h)2 + (y+k)2 = r2
d. X2 - y2 = r2
8. The standard equation of a circle with the center not at the origin of a coordinate system
is:
a. (x-h)2 + (y-k)2 = r2
b. X2 + y2 = r2
c. (x+h)2 + (y+k)2 = r2
d. X2 - y2 = r2
9. Find the center and the radius of the circle whose equation is (x-4)2 + (y+4)2 = 81
a. (-4, -4), r= 81
b. (-4, 4), r=9
c. ( 4, -4), r=9
d. ( 4, -4), r=81
10. Match the following conditions with the given statement
a. Given the radius, find diameter
C = 𝜋d _____d___
b. Given the diameter, find radius
A = 𝜋r2 ____e_____
c. Given the radius, find Circumference
d = 2r _____a_____
d. Given the diameter, find Circumference
C = 2𝜋𝑟 _____c____
e. Given radius, find Area
r = 𝜋𝑑 ______b_______
11. The Circumference of a circle whose equation is (x-9)2 + (y-3)2 = 49 is:
a. C= 98𝜋
b. C=49𝜋
c. C= 7𝜋
d. C =14𝝅
12. The Area of a circle whose equation is (x-9)2 + (y-3)2 = 49 is:
a. A= 98𝜋
b. A=49𝝅
c. A= 7𝜋
d. A =14𝜋
13. The Diameter of a circle whose equation is (x-9)2 + (y-3)2 = 49 is:
a. d= 98
b. d= 7
c. d =14
d. d = 49
14. How many points are both 2 centimeters from line
point P is on line l.
and 1 centimeter from point P,
1) 1
2) 2
3) 0
4) 4
15. The distance between points P and Q is eight (8) units. How many points are equidistant
from P and Q and also three (3) units from P?
1) 1
2) 2
3) 0
4) 4
16. The distance between parallel lines and m is 12 units. Point A is on line . How many
points are equidistant from lines and m and 8 units from point A.
1) 1
2) 2
3) 3
4) 4
17. What is the total number of points equidistant from two intersecting straight roads and
also 300 feet from the traffic light at the center of the intersection?
1) 1
2) 2
3) 3
4) 4
18. How many points are equidistant from two parallel lines and also equidistant from two
points on one of the lines?
1) 1
2) 2
3) 3
4) 4
19. In a coordinate plane, how many points are both 5 units from the origin and 2 units from
the x-axis?
1) 1
2) 2
3) 3
4) 4
20. How many points are both 4 units from the origin and also 2 units from the line
?
1) 1
2) 2
3) 3
4) 4
21. In the coordinate plane, what is the total number of points 5 units from the origin and
equidistant from both the x- and y-axes?
1) 1
2) 2
3) 0
4) 4
SKETCH LOCUS
1. In the diagram below, town C lies on straight road p. Sketch the points that are 2 miles from town C.
Then sketch the points that are 1 miles from road p. How many points satisfy both conditions?
2. Graph the locus of points equidistant from the x-axis and y-axis. On the same set of axes, graph the locus
of points 3 units from the line
. Label with an X all points that satisfy both conditions.
3. On the grid below, graph the points that are equidistant from both the x and y axes and the points that are
5 units from the origin. Label with an X all points that satisfy both conditions.
4. On the set of axes below, sketch the points that are 5 units from the origin and sketch the points that are 2
units from the line
. Label with an X all points that satisfy both conditions.