Mechanical Engineering Review Online

1. Find the equation of circle passing through (-5, 4) and center at (5, 4).

a. (x - 5)² + (y - 4)² = 100

b. x² - 15x + y² - 8y = 82

c. x² - 10x + y² - 12y = 80

d. (x - 5)² + (y - 4)² = 120

2. The shortest distance from A (4, 9) to the circle x2 + y2 + 4x + 6y = 14.

a. 13.4

b. 12.2

c. 15.8

d. 10.8

3. What is the coordinate of the center of the curve x2 + y2 – 3x -5y – 35 = 0?

a. (1.5, 2.5)

b. (-2.3, 3.3)

c. (1, 2)

d. (2.5, 1.5)

4. What is the distance between center of the circle x² + y² – 7y = 0 and x² – 6x + y² – 6y – 14 = 0?

a. 3

b. 4

c. 2

d. 5

5. What is the radius of a circle with the following equation? x² – 8x + y² – 6y – 15 = 0.

a. 6.3

b. 5.3

c. 4.2

d. 2.8

6. Find the center of the circle given by the equation x² + y² – 6x + 3y = 10.

a. (-2, 1.5)

b. (1.5, 2.5)

c. (3.5, 1.5)

d. (3, -1.5)

7. The equation of the circle on the x-y plane is given by x² – 3x + y² + 3y = 3. The center and the radius of the circle are _____, respectively.

a. C(2, 2.5), r=2.2

b. C(-1.5, -1.5), r=2.1

c. C(1.5, -1.5), r=2.7

d. C(2.5, -2.5), r=2.5

8. Find the standard equation of a circle whose center is at (2, 3) and passes through (6, 5).

a. x² + y² - 5x - 8y + 6 = 0

b.  x² + y² + 6x - 9y + 6 = 0

c.  x² + y² - 4x - 6y - 7 = 0

d.  x² + y² - 8x - 9y + 7 = 0

9. What is the radius of the circle described by x² – 3x + y² – 4y – 6 = 0?

a. 4.8

b. 2.2

c. 5.0

d. 3.5

10. The length of the latus rectum for the ellipse x²/49 + y²/25 = 1 is equal to ____.

a. 7.1

b. 6.2

c. 8.1

d. 5.4

11. Find the equation of the directrix of the parabola y² = 18x

a. 4

b. -4.5

c. 4.5

d. -4

12. The focus of the parabola y² = 24x is at _____.

a. (5, 0)

b. (3, 0)

c. (6, 0)

d. (2, 0)

13. The equation x2 – 10y2 + 8x – 4y + 8 = 0 is:

a. Hyperbola

b. Circle

c. Parabola

d. Ellipse

14. The equation y² + y – 4x + 8 = 0 opens:

a. to the left

b. to the right

c. upward

d. downward

15. The equation y² + y – 4x + 8 = 0 is:

a. Hyperbola

b. Circle

c. Parabola

d. Ellipse

16. If B² – 4AC = 0, then the equation of conic is:

a. Hyperbola

b. Circle

c. Ellipse

d. Parabola

17. An ellipse has a major axis of 10 and minor axis of 8. Find the eccentricity of the ellipse.

a. 0.6

b. 0.5

c. 0.7

d. 0.8

18. What is the equation of an ellipse with eccentricity (35/50)^0.5 and ends of minor axis at (0, ±5).

a. (x²/280) + (y²/28) = 1

b. (3x²/250) + (y²/25) = 1

c. (5x²/280) + (y²/20) = 1

d. (9x²/200) + (y²/38) = 1

19. What is the equation of an ellipse with foci at (±5, 0) and major axis of length 16.

a. 40x² - 65y² = 2652

b. 39x² + 60y² = 2229

c. 39x² + 64y² = 2496

d. 35x² + 63y² = 2042

20. What conic section is described by the following equation 10x² + 18y² + 54x – 64y = -1?

a. Hyperbola

b. Circle

c. Ellipse

d. Parabola

21. Find the equation of parabola with focus at (-2, 3) and directrix at y = -3.

a. (x-2)² = 10y

b. (x+3)² = -8y

c. (x-1)² = 16y

d. (x+2)² = 12y

22. Find the equation of parabola with vertex at (3, 4) and directrix at x = 6.

a. (x-4)² = 12(y+3)

b. (y+4)² = -12(x+3)

c. (y-4)² = -12(x-3)

d. (x-5)² = 12(y-3)

23. Find the eccentricity of a parabola whose equation is y² = 8(x – 7).

a. 0.30

b. 0.81

c. 1.0

d. 0.52

24. Find the angle between vectors V1(4i – j + 3k) and V2(i – 3j – 5k)

a. 122.4 deg

b. 136.2 deg

c. 105.4 deg

d. 148.7 deg

25. Given the vector V = i + 3j + k, what is the angle between V and the x – axis?

a. 65.35 deg

b. 43.81 deg

c. 57.51 deg

d. 72.45 deg

26. A sphere has a radius of 5m and center at (12, 12, 12). What is the surface area.

a. 314.2 m²

b. 221.28 m²

c. 368.11 m²

d. 287.27 m²

27. What is the distance from the plane 3x + 3y – 2z – 7 = 0 to the point (3, 3, -5)?

a. 3.8

b. 4.5

c. 2.1

d. 5.7

28. Find the radius of sphere passing through point (2, 6, 3)

a. 6

b. 5

c. 7

d. 8

29. What is the distance between two points (2, -4, 10) and (-5, 6, -8)?

a. 18.3

b. 16.2

c. 25.8

d. 21.7

30. What acute angle between vectors V1 (2, 3, 2) and V2 (3, 2, 4) based at the origin?

a. 20.8 deg

b. 28.7 deg

c. 25.7 deg

d. 22.8 deg

31. Find the distance between points in polar coordinates (6, 30^o) and (3, 80^o)

a. 3.8

b. 6.3

c. 5.8

d. 4.7

32. Find the length of vector (2, 4, -5).

a. 8.8

b. 5.5

c. 6.7

d. 7.5

33. The equation x² + 5y + 3xy + 4x – 3y – 12 = 0 is an equation of ____.

a. Parabola

b. Circle

c. Hyperbola

d. Ellipse

34. Find the x and y coordinate of (8, 40^o)

a. (6.1, 5.1)

b. (4.3, 6.6)

c. (7.9, 5.0)

d. (6.1, 4.5)

35. Find the polar form of x² + y² – 4x + 8y = 0

a. r = 4(cosθ - 2sinθ)

b. r = 6(cosθ + 2sinθ)

c. r = -3(2cosθ - sinθ)

d. r = 4(2cosθ - cos²θ)

36. The angle between vector V=3i – 6j + 8k and the x, y, and z axis is _____, respectively.

a. 40 deg

b. 45 deg

c. 32 deg

d. 38 deg

37. Find the eccentricity of an ellipse x² + 6y² = 8.

a. 0.21

b. 0.99

c. 0.76

d. 0.38

38. Find the eccentricity of hyperbola 10x² – 6y² = -40.

a. 2.8

b. 1.3

c. 0.68

d. 1.8

39. Find the equation of parabola with focus at (0, 6) and directrix at x=8.

a. y² + 10y - 12x - 33 = 0

b. y² - 8y - 14x + 28 = 0

c. 2y² - 17y - 13x - 35 = 0

d.  y² - 12y + 16x - 28 = 0

Answer Key (Handwritten)