University:
Felician University
Course:
MATH-231 | Geometry I
Academic year:

2022
Views:

137

Pages:

3
Author:

StellarSymphony

Answers to Conic Sections Review 1) 2) y 8 6 4 2 ( 19 4 Eccentricity: 1 2 4 6 8 x Focus: -5, - -8 -6 -4 -2 -2 -4 -6 -8 3) Hyperbola ( x + 3) 2 y 2 8 6 4 2 -2 -4 -6 -8 Ellipse ( x - 3) 2 14) 100 - ( x + 9) 2 196 12) =1 + ( ) 11 4 Eccentricity: 1 2 4 6 8 x -2 -4 -6 -8 y Hyperbola x 2 ( y + 2) 2 8 6 4 2 2 25 + y -8 -6 -4 -2 -2 -4 -6 -8 121 15) y = -( x + 2) 2 + 9 13) =1 29 » 1.077 5 Eccentricity: 8 6 4 2 =1 4 2 4 6 8 x -2 -4 -6 -8 ( x + 1 ) 2 ( y - 9) 2 - Center: (0, -2) Vertices: (5, -2), (-5, -2) Foci: ( 29 , -2), (- 29 , -2) -8 -6 -4 -2 ( y + 1) 2 49 =1 Parabola y = -( x - 6 ) 2 + 3 Vertex: (6, 3) Focus: 6, -8 -6 -4 -2 =1 36 Center: (3, -1) Vertices: (3, 5), (3, -7) Foci: (3, -1 + 4 2 ), (3, -1 - 4 2 ) 2 4 6 8 x 2 2 Eccentricity: » 0.943 3 4 11) ( x + 3) 2 + y 2 = 241 ( y - 8) 2 y 10) y 25 2 4 6 8 x 3 Eccentricity: = 0.6 5 8 6 4 2 7 7 + y+ =4 x+ 2 2 7 7 Center: - , 2 2 Radius: 2 2 4 6 8 xEccentricity: 0 -2 -4 -6 -8 ( y - 1) 2 + Center: (1, 1) Vertices: (1, 6), (1, -4) Foci: (1, 4), (1, -2) -2 -4 -6 -8 8) ( ) ( ) ( ) Ellipse ( x - 1) 2 16 -8 -6 -4 -2 Circle 2 -8 -6 -4 -2 -8 -6 -4 -2 =1 ( ) 8 6 4 2 8 6 4 2 y Circle y ( ) 8 6 4 2 ( ) -2 -4 -6 -8 1( y - 4) 2 - 3 3 Vertex: (-3, 4) 9 Focus: - , 4 4 2 4 6 8 xEccentricity: 1 -2 -4 -6 -8 3 2 ( + y - 4) 2 = 7 x+ 2 3 Center: - , 4 2 Radius: 7 2 4 6 8 xEccentricity: 0 -8 -6 -4 -2 Parabola x= -8 -6 -4 -2 6) y 9) ) 25 Center: (-3, 0) Vertices: (-1, 0), (-5, 0) Foci: (-3 + 29 , 0), (-3 - 29 , 0) 2 4 6 8 x 29 Eccentricity: » 2.693 2 -2 -4 -6 -8 7) - 4 -8 -6 -4 -2 5) 8 6 4 2 4) y 8 6 4 2 y Parabola y = ( x + 5) 2 - 5 Vertex: (-5, -5) Ellipse ( x - 3) 2 9 + ( y - 1) 2 36 =1 Center: (3, 1) Vertices: (3, 7), (3, -5) Foci: (3, 1 + 3 3 ), (3, 1 - 3 3 ) 2 4 6 8 x Eccentricity: ( x + 1) 2 ( y - 10) 2 + 81 100 1( 16) y = x - 5) 2 - 8 2 3 » 0.866 2 =1 X. Conic Sections Review Name___________________________________ Date________________ Period____ Classify each conic section, write its equation in standard form, and sketch its graph. For parabolas, identify the vertex, focus, and eccentricity. For circles, identify the center, radius, and eccentricity. For ellipses and hyperbolas identify the center, vertices, foci, and eccentricity. 1) - x 2 + y = 20 + 10 x 2) 0 = 7 - 3 x + y 2 - 8 y 3) 25 x 2 - 4 y 2 + 125 + 150 x = 0 4) 0 = 50 x - 25 x 2 + 32 y + 359 - 16 y 2 5) -32 y + 12 x + 45 + 4 x 2 = -4 y 2 6) y + x 2 = -33 + 12 x 7) 14 x = -2 x 2 - 41 - 2 y 2 - 14 y 8) 4 x 2 - 100 y = 200 + 25 y 2 9) y 2 - 54 x + 2 y = -46 - 9 x 2 10) 1 + 4 x 2 = 2 y + 24 x - y 2 Use the information provided to write the standard form equation of each circle. 11) Center: (-3, 0) Point on Circle: (-18, -4) Use the information provided to write the standard form equation of each ellipse. 12) Vertices: (-1, 20), (-1, -2) Foci: (-1, 9 + 6 2 ), (-1, 9 - 6 2 ) 19 10 ( Co-vertices: 8, 10), (-10, 10) 13) Eccentricity = Use the information provided to write the standard form equation of each hyperbola. 14) Foci: (-9, 8 + 2 74 ), (-9, 8 - 2 74 ) 5 7 101 7 5 11 y=- x+ 7 7 Asymptotes: y = x + Use the information provided to write the vertex form equation of each parabola. 15) Opens up or down, Vertex: (-2, 9), Passes through: (-5, 0) 16) Vertex: (5, -8), Directrix: y = - 17 2