Identify the equation as a parabola circle and ellipse

Assignment Help Engineering Mathematics

Reference no: EM131104526

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

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

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

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

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

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

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

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

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

Reference no: EM131104526

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