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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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