Download Linear and Circle Equations Review

Teacher: Mr. Santoro
Name: ____________________________________
Name: _________________________________ Date: __________
Common Core Geometry - Honors Circles/Equations - Review
1. Which graph represents a circle whose equation is x2 + (y – 1)2 = 9?
3. 1. 2. 4. 2. Which set of equations represents two circles that have the same center?
1. x2 + (y + 4)2 = 16 and (x + 4)2 + y2 = 16
2. (x + 3)2 + (y – 3)2 = 16 and (x – 3)2 + (y + 3)2 = 25
3. (x – 7)2 + (y – 2)2 = 16 and (x + 7)2 + (y + 2)2 = 25
4. (x – 2)2 + (y – 5)2 = 16 and (x – 2)2 + (y – 5)2 = 25
3. Which graph could be used to find the solution to the following system of equations?
y = (x + 3)2 – 1
x + y = 2
1. 3. 2. 4. 4. What are the coordinates of the center of a circle if the endpoints of its diameter are A(8, –4) and B(–3, 2)?
1. (2.5, 1) 3. (5.5, –3)
2. (2.5, –1) 4. (5.5, 3)
5. Write an equation of the line that is the perpendicular bisector of the line segment having endpoints (3, –1) and (3, 5).
[The use of the grid below is optional.]
6. On the set of axes below, solve the following system of equations graphically and state the coordinates of all points in the solution.
(x + 3)2 + (y – 2)2 = 25
2y + 4 = –x
7. What is an equation of the circle shown in the graph below?
1. (x – 3)2 + (y – 4)2 = 25
2. (x + 3)2 + (y + 4)2 = 25
3. (x – 3)2 + (y – 4)2 = 10
4. (x + 3)2 + (y + 4)2 = 10
8. The equation of a circle is (x − 2)2 + (y + 4)2 = 4. Which diagram is the graph of the circle?
1. 3. 2. 4. 9. Given the equations:
y = x2 − 6x + 10
y + x = 4
What is the solution to the given system of equations?
1. (2,3) 3. (2,2) and (1,3)
2. (3,2) 4. (2,2) and (3,1)
10. Which graph could be used to find the solution to the following system of equations?
y = –x + 2
y = x2
1. 3. 2. 4. 11. Solve the following system of equations algebraically:
9x2 + y2 = 9
3x - y = 3
The solution with a negative y value is: (
The solution with a non-negative y value is: (
, ).
, ).
12. The graphs of the equations y = x2 + 4x - 1 and y + 3 = x are drawn on the same set of axes. At which point do the
graphs intersect?
1. (1,4) 3. (-2,1)
2. (1,-2) 4. (-2,-5)
Answer Key for Linear and Circle Equations Review
1. 5.
1
9.
4
The first step is to find the midpoint of the segment created by connecting the two endpoints.
Second, find the slope of the segment.
The slope of the segment is undefined, which means that it is a vertical segment. Since the original segment is vertical, the
perpendicular bisector has to be horizontal. Horizontal lines have equations of the form y = a constant. The line has to pass
through the midpoint of the segment, which is (3, 2). So, the equation of the line is y = 2. It takes the y-value of the midpoint.
2. 6.
4
The equation, (x + 3)2 + (y – 2)2 = 25, is the equation of a circle whose center is at (–3, 2) and whose radius has the length of 5. Below is the graph of the circle.
10.
3
Now to graph the linear equation, 2y + 4 = –x, first put it into slope-intercept form of a line, y = mx + b.
The y-intercept is at the point (0, –2). Substitute another x-value or more into the equation of the line in order to find more points
to use when graphing the line.
x
y = − x − 2
y
−2
y = − (−2)− 2 = 1 − 2 = −1
−1
2
y = − (2)− 2 = −1 − 2 = −3
−3
Two other possible points are (–2, –1) and (2, –3). Plot these points and draw the line. Below is the graph with both equations.
The points of intersection are at (–8, 2) and (0, –2).
3. 7. 2
2
11.
0,
-3,
1,
0
4. 8. 2
2
12.
4