QUESTION 1. Find the vertices and locate the foci for the hyperbola whose equation is given.
81y2 - 64x2 = 5184
a. vertices: (-8, 0), (8, 0)
foci: (- , 0), ( , 0)
b. vertices: (0, -8), (0, 8)
foci: (0, - ), (0, )
c. vertices: (0, -9), (0, 9)
foci: (0, - ), (0, )
d. vertices: (-9, 0), (9, 0)
foci: (- , 0), ( , 0)
QUESTION 2. Find the vertices and locate the foci for the hyperbola whose equation is given.
49x2 - 16y2 = 784
a. vertices: (-4, 0), (4, 0)
foci: (- , 0), ( , 0)
b. vertices: (0, -4), (0, 4)
foci: (0, - ), (0, )
c. vertices: (-4, 0), (4, 0)
foci: (- , 0), ( , 0)
d. vertices: (-7, 0), (7, 0)
foci: (- , 0), ( , 0)
QUESTION 3. Find the standard form of the equation of the hyperbola satisfying the given conditions.
Center: (6, 5); Focus: (3, 5); Vertex: (5, 5)
a. - (y - 6)2 = 1
b. - (y - 5)2 = 1
c. (x - 5)2 - = 1
d. (x - 6)2 - = 1
QUESTION 4. Solve the problem.
An experimental model for a suspension bridge is built. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers are both 6.25 inches tall and stand 50 inches apart. At some point along the road from the lowest point of the cable, the cable is 1 inches above the roadway. Find the distance between that point and the base of the nearest tower.
10.2 in.
15 in.
9.8 in.
15.2 in.
QUESTION 5. Solve the problem.
An experimental model for a suspension bridge is built. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers stand 40 inches apart. At a point between the towers and 10 inches along the road from the base of one tower, the cable is 1 inches above the roadway. Find the height of the towers.
4 in.
4.5 in.
6 in.
3.5 in.
QUESTION 6. Find the standard form of the equation of the ellipse satisfying the given conditions.
Major axis vertical with length 16; length of minor axis = 6; center (0, 0)
+ = 1
+ = 1
+ = 1
+ = 1
QUESTION 7. Identify the equation as a parabola, circle, ellipse, or hyperbola.
12y = 3(x + 8)2
Circle
Hyperbola
Parabola
Ellipse
QUESTION 8. Find the vertices and locate the foci for the hyperbola whose equation is given.
y = ±
a. vertices: (0, -2 ), (0, 2 )
foci: (0, -2 ), (0, 2 )
b. vertices: (-2 , 0), (2 , 0)
foci: (-2 , 0), (2 , 0)
c. vertices: (-12, 0), (12, 0)
foci: (-2 , 0), (2 , 0)
d. vertices: (-12, 0), (12, 0)
foci: (-2 , 0), (2 , 0)
QUESTION 9. Find the standard form of the equation of the ellipse satisfying the given conditions.
Foci: (0, -2), (0, 2); y-intercepts: -3 and 3
+ = 1
+ = 1
+ = 1
+ = 1
QUESTION 10. Find the standard form of the equation of the parabola using the information given.
Vertex: (4, -7); Focus: (3, -7)
(y + 7)2 = -4(x - 4)
(x + 4)2 = -16(y - 7)
(x + 4)2 = 16(y - 7)
(y + 7)2 = 4(x - 4)
QUESTION 11. Find the standard form of the equation of the hyperbola satisfying the given conditions.
Endpoints of transverse axis: (0, -10), (0, 10); asymptote: y = x
- = 1
- = 1
- = 1
- = 1
QUESTION 12. Convert the equation to the standard form for a hyperbola by completing the square on x and y.
4y2 - 25x2 - 16y + 100x - 184 = 0
- = 1
- = 1
- = 1
- = 1
QUESTION 13. Find the standard form of the equation of the ellipse satisfying the given conditions.
Major axis horizontal with length 12; length of minor axis = 6; center (0, 0)
+ = 1
+ = 1
+ = 1
+ = 1
QUESTION 14. Find the standard form of the equation of the parabola using the information given.
Focus: (3, 3); Directrix: y = -5
(x - 3)2 = 16(y + 1)
(y + 1)2 = 16(x - 3)
(y - 3)2 = 16(x + 1)
(x + 1)2 = 16(y - 3)
QUESTION 15. Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate.
x2 - 6x - 6y - 21 = 0
(x + 3)2 = 6(y + 5)
(x - 3)2 = 6(y - 5)
(x - 3)2 = 6(y + 5)
(x + 3)2 = -6(y + 5)
QUESTION 16. Convert the equation to the standard form for a hyperbola by completing the square on x and y.
4x2 - 25y2 - 8x + 50y - 121 = 0
- = 1
- = 1
- = 1
- = 1
QUESTION 17. Find the standard form of the equation of the parabola using the information given.
Focus: (-3, -1); Directrix: x = 7
(x - 2)2 = -20(y + 1)
(y + 1)2 = -20(x - 2)
(y - 2)2 = -20(x + 1)
(x + 1)2 = -20(y - 2)
QUESTION 18. Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate.
y2 - 4y - 2x - 2 = 0
(y - 2)2 = 2(x + 3)
(y + 2)2 = -2(x + 3)
(y + 2)2 = 2(x + 3)
(y - 2)2 = 2(x - 3)
QUESTION 19. Identify the equation as a parabola, circle, ellipse, or hyperbola.
4x2 = 36 - 4y2
Parabola
Hyperbola
Ellipse
Circle
QUESTION 20. Find the standard form of the equation of the ellipse satisfying the given conditions.
Endpoints of major axis: (10, -3) and (-2, -3); endpoints of minor axis: (4, -1) and (4, -5)
+ = 1
+ = 1
+ = 0
+ = 1
QUESTION 21. Identify the equation as a parabola, circle, ellipse, or hyperbola.
2x = 2y2 - 30
Ellipse
Circle
Parabola
Hyperbola
QUESTION 22. Find the standard form of the equation of the hyperbola satisfying the given conditions.
Endpoints of transverse axis: (-6, 0), (6, 0); foci: (-7, 0), (-7, 0)
- = 1
- = 1
- = 1
- = 1
QUESTION 23. Find the standard form of the equation of the ellipse satisfying the given conditions.
Endpoints of major axis: and ; endpoints of minor axis: and
+ = 1
+ = 1
+ = 1
+ = 1
QUESTION 24. Identify the equation as a parabola, circle, ellipse, or hyperbola.
(x - 2)2 = 16 - y2
Circle
Ellipse
Hyperbola
Parabola
QUESTION 25. Identify the equation as a parabola, circle, ellipse, or hyperbola.
9x2 = 4y2 + 36
Hyperbola
Ellipse
Parabola
Circle