Conics X Point Line Two Intersecting Circle Parabola Hyperbola FIGURE 9 Degenerate Conics Convert from General form to Standard form then Graph and fill out pertinent Information 1) 4x2+ 9y2-16x + 54y + 61 = 0 Name: 2) 9x2 + 4y2 + 36x + 24y + 36=0 Name: Ellipse (x+2)2 + LY Ellipse Center: ( 2 , -2) Center: (-z ,-3) c2 = (big) -(small)2 c2 = (big)-(small) c2 = a2 - b2= 02= a2 - b2 = =9-4 = 9-4 ES CENS OCI: ( 2458 , -3 foci: ( eccentricity = % =15 eccentricity = = Major axis:2a =2(3)=6 Major axis:2a = Vertices: (243 , -3 Vertices: ( Minor axis:2b=2(2)=4 Minor axis:2b= co-vertices ( 2 ,-3+2) co-vertices ( area = nab=(2)()- area = nab= 671=02 3) x' + y2- 4x + 6y +4=0 Name: 4) y2 - 2y - 4x + 9 = 0 ( 4-1) = = 4 ( x-2 ) Name: Parabola (x-224 (+3)2 Center: (2 ,-3) Vertex: ( 2 , \\ ) ca = a2 - b2 4p =4 foci: ( 2 , -3 ) Vertex: ( eccentricity = =2=0 Focus: ( 3 , Major axis:2a Directrix: area = Tab eccentricity = = 5) 9x2-4y2+ 36x -24y - 36=0 (x+2)2 Name: Hyperbola 6) y2- x2 + 6y + 4x + 4=0 Name: _ (13=1 Center: (-2 , -3 ) Center: ( c2 = (pos)2+(neg)2 c2 = (pos)2+(neg)2 c2 = a2 + 62 c2 = a2 + 62 =4+9 C=1323.6 foci: (-2-413, -3 foci: ( asymptotes: asymptotes: y- y =1-(x-x,) ( x -x, ) Ax Ax 1+3 = + 2 ( x+2) eccentricity = % = ME eccentricity = = Transverse axis = 2a=4 Transverse axis = 2a conjugate axis = 2b=6 conjugate axis = 2b