Download Conics Test Review: Finding Centers, Radii, Equations, and Points of Conic Sections and more Summaries Pre-Calculus in PDF only on Docsity!
Conics Test REVIEW Name:_______________________________________
Pre-Calculus Hour:_______
Find the center and the exact radius of the circle. Then graph the circle.
2
2
2
2
25
9
Center:_________ Center:_________
Radius:_________ Radius:_________
Find the equation of the circle in standard form that satisfies the given conditions.
3. The circle has center
and 4. The circle has center
passes through (โ 3 , 4 ). and passes through (โ 1 , โ 1 ).
5. The endpoints of the diameter of the 6. The circle has center ( 4 , โ 3 ) and
circle are
and
. and is tangent to the x-axis.
Graph the ellipse and identify the center, vertices, and foci.
๐ฅ
2
9
๐ฆ
2
25
2
2
Center:___________ Center:___________
Vert:__________ Vert:__________
Foci:________ Foci:________
2
2
2
(๐ฆโ 3 )
2
4
Center:___________ Center:___________
Vert:__________ Vert:__________
Foci:________ Foci:________
( ๐ฅโ 1
)
2
4
( ๐ฆ+ 2
)
2
9
2
2
Center:___________ Center:___________
Vert:__________ Vert:__________
Foci:________ Foci:________
Find the standard form of the equation of each ellipse.
13. Foci ( 0 , ยฑ 3 ), vertices ( 0 , ยฑ 5 ) 14. Major axis horizontal with length 12 ;
length of minor axis 4 ; center: (โ 1 , 3 )
15. Foci (ยฑ 5 , 0 ), length of major axis 12 16. Endpoints of major axis: ( 2 , 2 ) & ( 8 , 2 )
Endpoints of minor axis: ( 5 , 3 ) & ( 5 , 1 )
Find the standard form of the equation of each hyperbola.
25. Foci ( 0 , ยฑ 4 ), vertices ( 0 , ยฑ 2 ) 26. Vertices (ยฑ 4 , 0 ), Asymptotes: ๐ฆ = ยฑ 3 ๐ฅ
27. Endpoints of transverse axis: (ยฑ 6 , 0 ) 28. Foci ( 0 , ยฑ 3 ), length of transverse axis 2
Asymptotes: ๐ฆ = ยฑ 2 ๐ฅ
Graph the parabola and identify the vertex, directrix, and focus.
2
2
Vertex: _______ Vertex: _______
Dir: _______ Dir: ____________
Focus: ___________ Focus:_________
2
2
Vertex: _______ Vertex: _______
Dir: ___________ Dir: __________
Focus: ________ Focus:________
2
2
Vertex: _______ Vertex: _______
Dir: _______ Dir: ____________
Focus: ___________ Focus:_________
Write an equation in standard form for the parabola satisfying the given conditions.
37. Focus: ( 9 , 0 ); Directrix: ๐ฅ = โ 9 38. Focus: (โ 10 , 0 ); Directrix: ๐ฅ = 10
39. Vertex: ( 5 , โ 2 ); Focus ( 7 , โ 2 ) 40. Focus: ( 2 , 4 ); Directrix: ๐ฅ = โ 4
Answers to Conics Test Review Name:________________________________
Pre-Calculus Hour:_____
1. Center:
; Radius: 3 2. Center:
; Radius:
5
3
2
2
2
2
2
2
2
2
7. C: ( 0 , 0 ); V: ( 0 , ยฑ 5 ); F: ( 0 , ยฑ 4 ) 8. C: ( 0 , 0 ); V: (ยฑ 3 , 0 ); F: (ยฑโ 5 , 0 ) 9. C: ( 0 , 0 ); V: (ยฑ 6 , 0 ); F: (ยฑ 3 โ 3 , 0 )
10. C: (โ 1 , 3 ); V: (โ 1 , 5 ), (โ 1 , 1 ); F: (โ 1 , 3 ยฑ
3 ) 11. C: ( 1 , โ 2 ); V: ( 1 , 1 ), ( 1 , โ 5 ); F: ( 1 , โ 2 ยฑ โ 5 )
12. C: (โ 4 , โ 3 ); V: (โ 4 , 3 ), (โ 4 , โ 9 ); F: (โ 4 , โ 3 ยฑ โ 35 ) 13.
๐ฅ
2
16
๐ฆ
2
25
(๐ฅ+ 1 )
2
36
(๐ฆโ 3 )
2
4
๐ฅ
2
36
๐ฆ
2
11
(๐ฅโ 5 )
2
9
(๐ฆโ 2 )
2
1
(๐ฅ+ 1 )
2
9
๐ฆ
2
25
(๐ฅโ 2 )
2
9
(๐ฆ+ 1 )
2
4
19. C: ( 0 , 0 ); V: ( 0 , ยฑ 3 ); F: ( 0 , ยฑ 5 ); A: ยฑ
3
4
20. C: ( 0 , 0 ); V: (ยฑ 2 , 0 ); F: (ยฑ 2
5 , 0 ); A: ยฑ
4
2
21. C: ( 1 , โ 2 ); V:
; F: ( 1 ยฑ โ 13 , โ 2 ); A: ยฑ
2
3
22. C: ( 2 , โ 1 ); V: ( 2 , 4 ), ( 2 , โ 6 ); F: ( 2 , โ 1 ยฑ โ 34 ); A: ยฑ
5
3
23. C: ( 3 , โ 2 ); V: ( 3 , 3 ), ( 3 , โ 7 ); F:
; A: ยฑ
5
4
24. C: ( 2 , โ 3 ); V: (โ 3 , โ 3 ), ( 7 , โ 3 ); F:
; A: ยฑ
4
5
๐ฆ
2
4
๐ฅ
2
12
๐ฅ
2
16
๐ฆ
2
144
๐ฅ
2
36
๐ฆ
2
144
๐ฆ
2
1
๐ฅ
2
8
(๐ฅโ 2 )
2
4
(๐ฆโ 1 )
2
9
๐ฆ
2
9
๐ฅ
2
1
31. V:
; D: ๐ฅ = 3 ; F:
32. V:
; D: ๐ฆ = โ 2 ; F:
33 .V:
; D: ๐ฆ = 3. 5 ; F:
34. V:
; D: ๐ฅ = โ 5 ; F:
35. V:
; D: ๐ฆ = 0 ; F:
36. V:
; D: ๐ฅ = 2 ; F:
2
2
2
2
2
2
2
; Parabola; V:
(๐ฆโ 1 )
2
4
(๐ฅโ 3 )
2
9
= 1 ; Hyperbola; C:
(๐ฅโ 4 )
2
9
(๐ฆ+ 2 )
2
4
= 1 ; Ellipse; C:
(๐ฅโ 1 )
2
16
(๐ฆ+ 2 )
2
9
= 1 ; Ellipse; C:
(๐ฅ+ 4 )
2
4
(๐ฆโ 3 )
2
16
= 1 ; Hyperbola; C:
2
2
= 26 ; Circle; C: ( 3 , โ 4 ) 49. (๐ฅ โ 3 )
2
2
= 26 ; Circle; C: ( 3 , โ 4 )
2
= 4 (๐ฅ + 2 ); Parabola; V: (โ 2 , โ 4 )
