Name: Date: Practice Final Exam Part II covering sections a108. As you try these problems, keep referring to your formula sheet.
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1 Name: Date: Practice Final Eam Part II covering sections a108 As ou tr these problems, keep referring to our formula sheet. 1. Find the standard form of the equation of the circle with center at the origin and radius 4. = + = + = 4 = 4 = 4. Identif the center and radius of the circle = 0. Center: (, ) Radius: 10 Center: (, ) Radius: 10 Center: (, ) Radius: Center: (, ) Radius: Center: ( 6, 6) Radius: 19. Find the -intercepts of the graph of the circle ( ) ( ) + +1 = , 15 1+, , , , Find the standard form of the parabola with focus (0,1) and verte at the origin. = 4 = = = 4 = 5. Find the verte and focus of the parabola 1 = 0 verte: (, 0 ) focus: (0, 0) verte: (0, 0) focus: ( 0, ) verte: (, 0 ) focus: (0, 0) verte: (0, 0) focus: ( 0, ) verte: (0, 0) focus: (, 0 ) Page 1
2 6. Match the graph with its equation. 7. Find the verte and focus of the parabola 1 Verte:, 11 Focus:, 1 Verte:, 15 Focus:, 1 Verte:, 1 Focus:, 1 Verte:, 5 Focus:, 1 Verte:, 5 Focus:, = 0. Page
3 8. Find the standard form of the parabola with the given characteristics: focus: (9, 16) & verte: (9, 7) ( 9) = 6( + 7) ( 7) = 6( + 9) ( + 9) = 6( 7) ( + 9) = 9( 7) ( + 7) = 6( 9) 9. Find the center and vertices of the ellipse = 0. center: (7, 8) vertices: (5, 8), (9, 8) center: ( 8, 7) vertices: ( 9, 7), ( 7, 7) center: (8, 7) vertices: (7, 7), (9, 7) center: (8, 7) vertices: (6, 7), (10, 7) center: ( 8, 7) vertices: ( 10, 7), ( 6, 7) 10. (OMIT) Find the eccentricit of the following ellipse. Round our answer to two decimals = Find the standard form of the equation of the ellipse below = 0 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Find the standard form of the equation of the ellipse centered at the origin having vertices at ( 7,0) and ( 7,0 ) and foci at ( 6,0) and ( 6,0 ). ( 1) Page
4 1. Find the standard form of the equation of the ellipse with the following characteristics. foci: ( ±,0) major ais of length: Find the standard form of the equation of the ellipse with the given characteristics. vertices: (, ), (, 7) minor ais of length: 8 ( + ) ( + ) 16 5 ( ) ( ) 16 5 ( ) ( ) 5 16 ( ) ( ) 5 16 ( + ) ( + ) Find the standard form of the equation of the ellipse having foci at ( 0,0 ) and ( 0,8 ) and major ais of length 18. ( + 4) 65 9 ( 4) 9 65 ( 4) 9 65 ( + 4) ( 65) ( 65) 9 ( 4) Find the standard form of the equation of the ellipse with the given characteristics. foci: ( 8, ), ( 8, 8) endpoints of the major ais: ( 8, 1), ( 8, 11) ( 8 ) ( + 5) 7 6 ( + 8 ) ( 5) 7 6 ( + 8 ) ( 5) 6 7 ( 5 ) ( + 8) 6 7 ( + 5 ) ( 8) 6 7 Page 4
5 17. (OMIT) Find the standard form or the equation of the ellipse with vertices (±8, 0) and eccentricit e = Match the graph with its equation. Page 5
6 19. Find the center and foci of the hperbola. ( 4 ) ( 9) 9 7 center: ( 9, 4) foci: ( 9, 8), ( 9, 0) center: (9, 4) foci: (9, 0), (9, 8) center: (4, 9) foci: (0, 9), (8, 9) center: (9, 4) foci: (5, 4), (1, 4) center: ( 4, 9) foci: ( 4, 1), ( 4, 5) 0. Find the standard form of the equation of the hperbola 5 = 15. = ( ) ( 5) 1 ( ) ( 5) 1. Find the vertices and asmptotes of the hperbola 5 9 = 5. vertices: (0, ±) asmptote: = ± 5 5 vertices: (0, ±) asmptote: = ± vertices: (±, 0) asmptote: = ± 5 5 vertices: (±, 0) asmptote: = ± vertices: (±, 5) asmptote: = ± 5. Find the standard form of the equation of the hperbola = 0. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Page 6
7 . Find the center and vertices of the hperbola = 0. center: ( 4, 5) vertices: ( 4, 7), ( 4, ) center: (4, 5) vertices: (4, ), (4, 7) center: (4, 5) vertices: (, 5), (6, 5) center: ( 4, 5) vertices: ( 6, 5), (, 5) center: ( 5, 4) vertices: ( 7, 4), (, 4) 4. Find the standard form of the equation of the hperbola with the given characteristics. vertices: (0, ±4) foci: (0, ±7) = = (OMIT) Find the standard form of the equation of the hperbola with the given characteristics. foci: (±5, 0) asmptotes: = ± Find the standard form of the equation of the hperbola with the given characteristics. vertices: (1, 5), (1, 1) foci: (1, 8), (1, 4) ( + ) ( 1) 9 7 ( ) ( + 1) 9 7 ( + 1 ) ( ) 7 9 ( + ) ( 1) 9 6 ( ) ( + 1) Classif the graph of the equation as a circle, a parabola, an ellipse, or a hperbola = 0 ellipse parabola hperbola circle 8. Classif the graph of the equation below as a circle, a parabola, an ellipse, or a hperbola = 0 ellipse parabola hperbola circle Page 7
8 9. Classif the graph of the equation below as a circle, a parabola, an ellipse, or a hperbola = 0 hperbola circle ellipse parabola 0. Find an points of intersection of the graphs algebraicall. ( 6, ), ( 0, ) ( 6, ), ( 0, ) (, 0 ), (, 4) ( 6, ), ( 0, ) ( 6, ), ( 0, ) = = 0 Page 8
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