WorksheetsCE-IC 411 || QUIZ NO. 4 - ANALYTIC GEOMETRY
Total questions: 61
Worksheet time: 31mins
Name
Class
Date
1.
First Name M.I. Last Name
4 lines
2.
Find the distance between the points A (1,9, -6) and B (1, 8, -7).
a)
A. 1.313
b)
B. 1.414
c)
C. 1.732
d)
D. 1.778
3.
Find the angle between the lines AB and CD. A (-3, 2, 4), В (2, 5, -2) and C (1, -2, 2), D (4, 2, 3).
a)
A. 62.44°
b)
B. 58.55°
c)
C. 65.43°
d)
D. 60.51°
4.
Find the Direction Cosine of the line that is perpendicular to each of the two lines whose directions are <3 0 1> and <2 -1 2>
a)
A. <0.196 0.784 -0.858>
b)
B. <0.169 -0.784 0.585>
c)
C. <0.196 -0.784 -0.588>
d)
D. <0.169 -0.784 -0.588>
5.
Determine the value of k and q so that ABC are collinear A(1, 0, -2), B(3, -1, 1) and C(k, -3, q) are collinear.
a)
A. -7,0
b)
B. 7,7
c)
C. 0,5
d)
D. 5, 7
6.
Find the coordinates of the foot of the perpendicular from A (1, 1, 1) on the line joining B (1, 4, 6) and C (5, 4, 4).
a)
A. (5, 12,13)
b)
B. (3, 4, 5)
c)
C. (3, -4, 5)
d)
D. (4, 3, 5)
7.
Find the coordinates of the foot of the perpendicular drawn from the point (3,4,5) to the x-axis.
a)
A. (3, 0, 0)
b)
B. (3, 0,5)
c)
C. (3, -4, 0)
d)
D. (3, 4, 0)
8.
Find the coordinates of the point where the segment joining the points (2, -2,1) and (5,1, -2) crosses the xy-plane.
a)
A. (3, 1, 0)
b)
B. (-3, 1, 0)
c)
C. (3, -1, 0)
d)
D. (-3, -1, 0)
9.
Find the points that trisect the segment joining the points (3, -1,5) and (0,5, -4).
a)
A. (2, -1, 3), (1, 3, 2)
b)
B. (2, 1, 2), (1, 3, -1)
c)
C. (-2, 1, 2), (-3, 1, 1)
d)
D. (1, 3, 1), (2, 1, 2)
10.
Find the equation of the plane through P (4, 3, 6) and perpendicular to the line joining P (4, 3, 6) to the point Q (2, 3, 1).
a)
A. 2x + 5z - 38 = 0
b)
B. 5x + 2z - 12 = 0
c)
C. 5x - 2z + 45 = 0
d)
D. 3x + 5z - 20 = 0
11.
Find the equation of the plane through the point P (1, 2, -1) and parallel to the plane 2x - 3y + 4z + 6 =0.
a)
A. 2x - 3y + 4z + 8 = 0
b)
B. 3x + y - 8z + 6 = 0
c)
C. 7x - 6y + 4z = 0
d)
D. 5x + 5y + 2z + 15 = 0
12.
Find the equation of the plane that contains the three points P (1, -2, 4), Q(4, 1, 7), R (-1, 5, 1).
a)
A. 2x + 5y + 6z + 12 = 0
b)
B. 10x - y - 9z + 24 = 0
c)
C. 10x - 2y - 9z - 24 = 0
d)
D. 2x + 5y + 6z - 12 = 0
13.
Find the perpendicular distance between the point (-2, 8, -3) and plane 9x - y -4z + 1 = 0.
a)
A. 1.313
b)
B. 1.414
c)
C. 1.732
d)
D. 1.778
14.
Find the perpendicular distance between the two planes x - 2y + 2z = 6, 3x -6y + 6z = 2.
a)
A. 2.828
b)
B. 1.414
c)
C. 1.732
d)
D. 1.778
15.
Find the equation of the line through the following points (1, 3, -2), (2, 2, 0), in parametric form.
a)
A. x = t + 1, y = -t + 3, z = 2t - 2
b)
B. x = -t + 1, y = 2t + 3, z = t + 2
c)
C. x = t - 1, y = t + 3, z = 2t + 2
d)
D. x = t + 1, y = t - 3, z = 2t - 1
16.
Find the point on the line x = y = z, that is equidistant from the points (3 , 0, 5) and (1, -1, 4).
a)
A. (0, 0, 0)
b)
B. (-2, -2, -2)
c)
C. (1, 1, 1)
d)
D. (2, 2, 2)
17.
Find the center and radius of the sphere whose equation is x² + y² + z² = 6x + 8z.
a)
A. (-3, 0, -4); r = 5
b)
B. (3, 0, 4); r = 5
c)
C. (-3, 0, -4); r = 25
d)
D. (3, 0, 4); r = 25
18.
Find the equation of the sphere tangent to the plane 6x + 6y + 7z = 22, and has its center at origin and point of tangency.
a)
A. x² + y² + z² = 1
b)
B. x² + y² + z² = 9
c)
C. x² + y² + z² = 4
d)
D. x² + y² + z² = 16
19.
Find the slope of the line 3x - 2y + 3 = 0.
a)
A. 3/2
b)
B. 2/3
c)
C. -3/2
d)
D. -2/3
20.
Compute for the acute angle between the lines whose slopes are, m₁ = 1/3 and m₂ = 2.
a)
A. 45°
b)
B. 60°
c)
C. 22.456°
d)
D. 54.162°
21.
What is the acute angle formed between the lines 4x - y + 3 = 0 and 2x - 5y - 1 = 0?
a)
A. 45°
b)
B. 60°
c)
C. 22.456°
d)
D. 54.162°
22.
Find the distance between the points A (-2,3) and B (6,8).
a)
A. 14.15
b)
B. 9.43
c)
C. 6.40
d)
D. 13.60
23.
Find the area of the triangle whose vertices are at points A (3,4), В (-2, 1) and C (5, -6).
a)
A. 56
b)
B. 14
c)
C. 28
d)
D. 26
24.
Find the shortest distance from point (2,3) to the line 3x + 2y - 5 = 0.
a)
A. 2.94
b)
B. 3.44
c)
C. 1.94
d)
D. 2.52
25.
What is the distance between the lines: 5x - 2y + 3 = 0 and 5x - 2y + 7 = 0?
a)
A. 0.743
b)
B. 1.346
c)
C. 0.190
d)
D. 5.385
26.
The curve x² + y² - 4x + 2y - 4 = 0 has its center at?
a)
A. (2, 1)
b)
B. (-2, -1)
c)
C. (2, -1)
d)
D. (-2, 1)
27.
What is the radius of the curve x² + y² - 6x - 8y - 11 = 0?
a)
A. 11
b)
B. 6
c)
C. 1
d)
D. 3
28.
Find the centroid of the triangle whose vertices are at points (3, 4), (6, -9) and (-6, 2).
a)
A. (1, 1)
b)
B. (1, -1)
c)
C. (-1, 1)
d)
D. (-1, -1)
29.
The equation of the line passing through points (2, 4) and (5, 8) is?
a)
A. 3x + 4y = -4
b)
B. 4x - 3y = -4
c)
C. 3x - 4y = 4
d)
D. 4x + 3y = 4
30.
Two lines 3x + 2y - 3 = 0 and Ax - 3y + 2 = 0 are perpendicular to each other. Determine the value of A.
a)
A. 2
b)
B. 0
c)
C. -2
d)
D. -1
31.
What is the equation of the line with slope equal to 3 and y-intercept of 5?
a)
A. y = 5x + 3
b)
B. y = 5x - 3
c)
C. y = -3x - 5
d)
D. y = 3x + 5
32.
What is the equation of the line that passes through the origin and perpendicular to the line 3x - 4y + 3 = 0?
a)
A. 3x + 4y = 0
b)
B. 3x - 4y = 0
c)
C. 4x - 3y = 0
d)
D. 4x + 3y = 0
33.
What is the equation of the line that passes through the origin and parallel to the line 5x - 2y + 3 = 0?
a)
A. 2x - 5y = 0
b)
B. 5x + 2y = 0
c)
C. 5x - 2y = 0
d)
D. 2x + 5y = 0
34.
A circle passes through the point (5, 7) and has its center at (2, 3). Find its equation.
a)
A. (x + 2)² + (y - 3)² = 25
b)
B. (x - 2)² + (y - 3)² = 25
c)
C. (x - 2)² + (y + 3)² = 25
d)
D. (x + 2)² + (y + 3)² = 25
35.
How far is the center of the circle x² + y² - 6x - 8y - 11 = 0 from the y-axis?
a)
A. 3
b)
B. 4
c)
C. 6
d)
D. 2
36.
Find the vertex of the parabola whose equation is y² - 2x - 4y + 2 = 0.
a)
A. (1, -2)
b)
B. (-1, 2)
c)
C. (2, -1)
d)
D. (2, 1)
37.
Determine the equation of the directrix of the parabola: y² = 16x.
a)
A. x = 4
b)
B. y = -4
c)
C. x = -4
d)
D. y = 4
38.
A parabola has an equation of x² - 4y - 2x + 8 = 0. Find the length of the latus rectum.
a)
A. 1
b)
B. 16
c)
C. 4
d)
D. 8
39.
A parabola has its vertex at (2, 4) and focus at (4, 4). Determine its equation.
a)
A. (y + 4)² = 4 (x - 2)
b)
B. (y + 4)² = 4(x + 2)
c)
C. (y - 4)² = 8 (x - 2)
d)
D. (y - 4)² = 8(x + 2)
40.
The eccentricity of a parabola is always equal to?
a)
A. 0
b)
B. greater than 1
c)
C. less than 1
d)
D. 1
41.
What is the eccentricity of an ellipse whose length of major and minor axes equal to 5 and 4, respectively, with center at origin?
a)
A. 5/3
b)
B. 4/5
c)
C. 3/5
d)
D. 3/4
42.
Find the second eccentricity of the curve 9x² + 4y² - 36x - 8y + 4 = 0.
a)
A. 2.24
b)
B. 0.89
c)
C. 1.12
d)
D. 0.45
43.
Convert r = 3cosθ into Cartesian coordinates.
a)
A. x² + y² - 3x = 0
b)
B. x² - y² - 3x = 0
c)
C. x² + y² + 3x = 0
d)
D. x² + y² + 3x = 0
44.
Convert x² + y² - 2x + 4y = 0 into polar form.
a)
A. 2r - 4cosθ - 2sinθ = 0
b)
B. r - 2cosθ + 4sinθ = 0
c)
C. 2 - 2sinθ - 4cosθ = 0
d)
D. 2 - 4cosθ + 2sinθ = 0
45.
Determine the polar coordinates of a point having a Cartesian coordinate of (3,4).
a)
A. 5∠53.13°
b)
B. -5∠53.13°
c)
C. 5∠-53.13°
d)
D. -5∠-53.13°
46.
Determine the Cartesian coordinate of a point having a polar coordinate of (12, 30°).
a)
A. (6, 10.392)
b)
B. (-6, -10.392)
c)
C. (10.392, -6)
d)
D. (10.392, 6)
47.
Determine the flatness of the ellipse 9x² + 4y² - 36x - 8y + 4 = 0.
a)
A. 1/2
b)
B. 5/4
c)
C. 2
d)
D. 4/5
48.
Find the distance between points (2, 3, 5) and (-1, 4, -2) in space.
a)
A. 7.86
b)
B. 7.68
c)
C. 8.67
d)
D. 6.78
49.
What is the radius of a sphere that passes through (1, 3, 6) and has its center at the origin?
a)
A. 7.86
b)
B. 7.68
c)
C. 8.67
d)
D. 6.78
50.
Determine the point of intersection of the planes: 4x - 3y + 2z = 7, x + 2y - z = 4 and 5x + y + 2z = 21.
a)
A. (-2, -3, -4)
b)
B. (3, 4, 2)
c)
C. (2, 3, 4)
d)
D. (-3, -4, -2)
51.
Find the distance between foci of the curve 9x² + 4y² - 36x - 8y + 4 = 0.
a)
A. 17.89
b)
B. 2.34
c)
C. 4.47
d)
D. 3.58
52.
The eccentricity of the curve 9x² - 4y² = 36 is?
a)
A. 1.20
b)
B. 3.61
c)
C. 0
d)
D. 1.80
53.
Find the locus of points such that the distance from (2, 3) to any point on the curve is twice the distance from the line x = 3 to that point on the curve.
a)
A. 3x² - y² + 20x + 6y + 23 = 0
b)
B. x² + 3y² + 20x - 6y + 23 = 0
c)
C. 3x² - 3y² - 20x + 6y + 23 = 0
d)
D. x² - 3y² - 20x + 6y + 23 = 0
54.
Find the new equation of the curve 5x - 2y = 2 if the origin is translated to the point (2, -3).
a)
A. 5x' + 2y' - 12 = 0
b)
B. 5x' - 2y' + 14 = 0
c)
C. 2x' - 5y' + 14 = 0
d)
D. 5x' + 2y' - 12 = 0
55.
Determine the new equation of the parabola y² - 6x + 4y + 22 = 0 if the origin is translated to its vertex.
a)
A. 6y'² = x'
b)
B. 6y'² = x'²
c)
C. y'² = 6x'
d)
D. y'² = 4x'²
56.
Find the point to which the origin must be translated in order that the transformed equation of the curve 4x² + 4y² - 8x + 4y + 1 = 0 will have no first-degree term.
a)
A. (1/2, 1)
b)
B. (1, -1/2)
c)
C. (1, 1/2)
d)
D. (-1/2, -1)
57.
Determine the new equation of the curve xy = 4 when the axes are rotated 45°.
a)
A. x'² - 8y'² = 1
b)
B. x'² - y'² = 8
c)
C. 4x'² - y'² = 1
d)
D. x'² + y'² = 4
58.
Find the new equation of the curve x² - 16y if the axes are rotated 30°.
a)
A. 3.46x'² - 3x'y' + y'² = x' + 55.43y'
b)
B. x'² - 3.46x'y' + y'² = 32x' + 55.43y’
c)
C. 3.46x′² -3x'y' + y'² = x' + 55.43y'
d)
D. 3x'² - 3.46x'y' + y'² = 32x′ + 55.43y’
59.
What is the new equation of the line 3x + 2y = 1 if the axes are rotated 60°?
a)
A. 3.20x' - 3.20y' = 16
b)
B. -6.46x′ + 3.20y' = 1
c)
C. 3.20x′ + 3.20y’ = 1
d)
D. 6.46x′ -3.20y’ = 2
60.
Determine the center of the sphere x² + y² + z² + 8x + 6y + 10z = 0.
a)
A. (4, 3, 5)
b)
B. (3, 5, 4)
c)
C. (-4, -3, -5)
d)
D. (-3, -5, -4)
61.
Find the radius of the sphere x² + y² + z² + 2x - 6y - 12z = 0.
a)
A. 8.76
b)
B. 6.78
c)
C. 7.86
d)
D. 3.39
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