Name _______________________________
Conics - Circles Review
1. Graph the following circle:
(x - 3)2 + (y + 1)2 = 4
2. Identify its center and radius.
(y + 8)2 + (x + 2)2 = 72
Center:_____________
Radius:_____________
3. Write the equation of the following circles:
4. Find the standard form, center, and radius of the following circle:
x2 + y2 – 4x + 8y – 5 = 0
Center___________________
Radius___________________
5.
Give the equation of the circle that is tangent to the y-axis and center is (-3, 2).
6. Graph the following circle:
x2 – 2x + y2 + 8y – 8 = 0
7.
Give the equation of the circle whose center is (5,-3) and goes through (2,5)
8.
Give the equation whose endpoints of a diameter at (-4,1) and (4, -5)
Write the standard equation of the circle described.
9. The center is (0, 0) and the radius is 9.
10. The center is (–5, 1) and the radius is 4.
Use the provided information in each problem that follows to solve.
11. Write the general equation of the circle with center (5, 0) and radius 3√2.
12. Find the center and radius of the circle described by the equation x2 + y2 + 6x – 4y – 27 = 0.
13. A particular cell phone tower is designed to service a 12-mile radius. The tower is located at (–3, 5) on a
coordinate plane whose units represent miles. What is the standard equation of the outer boundary of the
region serviced by the tower? Is a cell phone user at (8, 0) within the service range? Explain.
14. A pizza restaurant will deliver up to 5 miles. The restaurant is located at the origin on a coordinate plane
whose units represent miles. What is the standard equation of the outer boundary of the delivery region?
Customers are located at A (4, 3), B (5, 0), and C (2, √21 ). Which of these customers, if any, are on the
outer boundary? Explain.
15. Marco is a park ranger stationed in a fire tower. The tower is on a coordinate plane whose units
represent miles. Marco is responsible for monitoring a region whose boundary has the equation
x2 + y2 + 3x + y – 6.5 = 0. What is the geometric description of the region for which Marco is
responsible?