Center: (h, k) AOS: x = h and y = k Orientation: Horizontal if a >b Vertical if a<b Vertices: endpoints of major axis Covertices: endpoints of minor axis Foci: the points c distance from center Cone cut by a plane at an angle through the sides Real World: Tunnels Vertical Ellipse Horizontal Ellipse Major axis Minor axis b b b b aa a a

Steps to graph 1)Find center 2)Square root a 2 and b 2 3)Find c 4)Plot center 5)Count left and right a spaces 6)Count up and down b spaces 7)Connect those 4 with curve. 8)Count c spaces on major axis both directions to find Foci. Ex 3) Write the equation given the graph Ex 1) Graph Ellipse Steps to write equation 1)Find center 2)Find a and square it 3)Find b and square it 4)Substitute into formula. Center: (5, -2) a = b= c= Vertices: (1, -2) (9, -2) Covertices: (5, 1) (5, -5) AOS: x=5 and y=-2 Ex 2) Graph Center: (-3, 0) a = b= c= Vertices: (-3, 5) (-3, -5) Covertices: (-1, 0) (-5, 0) AOS: x=-3 and y=0 (x-axis) Center: (-1, -2) a = 3 b= 6

Change to Conic Form: Complete the Square 1 variable squared 2 variables squared Squared variable coefficient >1 Pre-AP Only x 2 + y 2 -2x - 4y – 4 = 0 (x 2 -2x + ___) + (y 2 - 4y + ____) = ____ + ____ (-2/2)=-1 then (-1) 2 =1 AND (-4/2)=-2 then (-2) 2 =4 (x 2 -2x + 1) + (y 2 - 4y + 4) = (x-1) 2 + (y-2) 2 = 1 9x 2 + 4y x - 8y – 59 = 0 9x x + 4y 2 - 8y = 59 9(x 2 - 6x +__) + 4(y 2 - 2y + __) = (__) + 4(__) (-6/2) 2 =9 and (-2/2) 2 =1 9(x 2 - 6x +9) + 4(y 2 - 2y + 1) = (9) + 4(1) 9(x – 3) 2 + 4(y – 1) 2 = 144 y 2 + x + 10y + 26 = 0 y y + ___ = -x – 26 + ___ (10/2)=5 then 5 2 =25 y y + 25 = -x – (y+5) 2 = -x – 1 (y+5) 2 = -(x +1) 6x x - y + 15 = 0 6x x + __ = y – 15 + ___ 6(x 2 + 2x + __) = y – (__) (2/2)=1 then 1 2 =1 6(x 2 + 2x + 1) = y – (1) 6(x+1) 2 = y – 9 1)GMA (Group, move, add blanks) 2)Fill in blanks 3)Factor and simplify 1)GMA (Group, move, add blanks) 2)Factor out GCF and add to blank on other side 3)Fill in blanks 4)Factor and simplify