1. 9.1-9.4 Circles and Parabolas Review

2. 9.1 Graphing and Writing Equations of Circles
Standard Form of a circle:
(𝑥−ℎ) 2 + (𝑦−𝑘) 2 = 𝑟 2
General Form of a circle: 𝐴 𝑥 2 +𝐵 𝑦 2 +𝐶𝑥+𝐷𝑦+𝐸=0
Given center and radius, graph and write the equation in standard form
Given a graph, identify the center and radius and write the equation in standard form
Convert from standard to general form
Convert from general to standard form (complete the square)

3. The center of a circle is at (2,3) and the radius is 2
The center of a circle is at (2,3) and the radius is 2. Graph the circle and write the equation in standard form.

4. Given the graph below, identify the center
and radius, and write the equation in
standard form.

5. Convert from standard to general form.
(𝑥−2) 2 + (𝑦+1) 2 =9

6. Convert from general to standard form.
𝑥 2 + 𝑦 2 +6𝑥−8𝑦+21=0

7. 9.2 Solving Simple Intersections – Lines & Circles
Solve by graphing
- Graph both equations
- Identify points of intersection
Solve algebraically
- Solve the linear for a variable
- Substitute the linear into the circle
- Solve for the variable
- Substitute your solutions into the linear
equation to find the other coordinate for
each solution/point.

8. Solve the system of equations by graphing.
(𝑥+1) 2 + (𝑦−1) 2 =9
(𝑥−2) 2 + (𝑦+2) 2 =9

9. Solve the system of equations algebraically.
𝑥 2 + 𝑦 2 =17
𝑥+𝑦=−3

10. 9.3 Graphing Parabolas as Conic Sections
Given the equation for a conic section/
parabola, identify the following and draw
the graph:
- Vertex
- p
- Focus
- Directrix
- Focal Width

11. Identify the items below and graph the
parabola.
𝑦+2= 1 8 (𝑥−3) 2
Vertex:________
p=_______
Focus:________
Directrix:___=_____
Focal Width:_______

12. 8. Identify the items below and graph the
parabola.
(𝑦−1) 2 =−12(𝑥+2)
Vertex:________
p=_______
Focus:________
Directrix:___=_____
Focal Width:_______

13. 9.4 Writing Equations of Parabolas
Given two pieces of information:
graph what you have
find the p-value
find the vertex (h,k)
write the equation

14. Write the equation of the parabola given that
the focus is at (-3,0) and the directrix is y=-4.

15. 10. Write the equation of the parabola given that
the vertex is (3,4) and the directrix is x=6.