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**9.1-9.4 Circles and Parabolas Review**

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**9.1 Graphing and Writing Equations of Circles**

Standard Form of a circle: (π₯ββ) 2 + (π¦βπ) 2 = π 2 General Form of a circle: π΄ π₯ 2 +π΅ π¦ 2 +πΆπ₯+π·π¦+πΈ=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)

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**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.

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**Given the graph below, identify the center**

and radius, and write the equation in standard form.

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**Convert from standard to general form.**

(π₯β2) 2 + (π¦+1) 2 =9

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**Convert from general to standard form.**

π₯ 2 + π¦ 2 +6π₯β8π¦+21=0

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**9.2 Solving Simple Intersections β 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.

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**Solve the system of equations by graphing.**

(π₯+1) 2 + (π¦β1) 2 =9 (π₯β2) 2 + (π¦+2) 2 =9

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**Solve the system of equations algebraically.**

π₯ 2 + π¦ 2 =17 π₯+π¦=β3

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**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

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**Identify the items below and graph the**

parabola. π¦+2= 1 8 (π₯β3) 2 Vertex:________ p=_______ Focus:________ Directrix:___=_____ Focal Width:_______

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**8. Identify the items below and graph the**

parabola. (π¦β1) 2 =β12(π₯+2) Vertex:________ p=_______ Focus:________ Directrix:___=_____ Focal Width:_______

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**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

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**Write the equation of the parabola given that**

the focus is at (-3,0) and the directrix is y=-4.

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**10. Write the equation of the parabola given that**

the vertex is (3,4) and the directrix is x=6.

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