2 9.1 Graphing and Writing Equations of Circles Standard Form of a circle:(𝑥−ℎ) 2 + (𝑦−𝑘) 2 = 𝑟 2General Form of a circle: 𝐴 𝑥 2 +𝐵 𝑦 2 +𝐶𝑥+𝐷𝑦+𝐸=0Given center and radius, graph and write the equation in standard formGiven a graph, identify the center and radius and write the equation in standard formConvert from standard to general formConvert 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 instandard 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 intersectionSolve algebraically- Solve the linear for a variable- Substitute the linear into the circle- Solve for the variable- Substitute your solutions into the linearequation to find the other coordinate foreach 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 =17𝑥+𝑦=−3
10 9.3 Graphing Parabolas as Conic Sections Given the equation for a conic section/parabola, identify the following and drawthe graph:- Vertex- p- Focus- Directrix- Focal Width
11 Identify the items below and graph the parabola.𝑦+2= 1 8 (𝑥−3) 2Vertex:________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 havefind the p-valuefind 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.