# Circles and Parabolas Review

## Presentation on theme: "Circles and Parabolas Review"β Presentation transcript:

9.1-9.4 Circles and Parabolas Review

9.1 Graphing and Writing Equations of Circles
Standard Form of a circle: (π₯ββ) 2 + (π¦βπ) 2 = π 2 General Form of a circle: π΄ π₯ 2 +π΅ π¦ 2 +πΆπ₯+π·π¦+πΈ=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)

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.

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

Convert from standard to general form.
(π₯β2) 2 + (π¦+1) 2 =9

Convert from general to standard form.
π₯ 2 + π¦ 2 +6π₯β8π¦+21=0

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.

Solve the system of equations by graphing.
(π₯+1) 2 + (π¦β1) 2 =9 (π₯β2) 2 + (π¦+2) 2 =9

Solve the system of equations algebraically.
π₯ 2 + π¦ 2 =17 π₯+π¦=β3

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

Identify the items below and graph the
parabola. π¦+2= 1 8 (π₯β3) 2 Vertex:________ p=_______ Focus:________ Directrix:___=_____ Focal Width:_______

8. Identify the items below and graph the
parabola. (π¦β1) 2 =β12(π₯+2) Vertex:________ p=_______ Focus:________ Directrix:___=_____ Focal Width:_______

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

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

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