MATH - Analytic Geometry

Quiz by Florenzo Miguel Aclan (Florencii)

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30 questions
• Q1
Find the direction of the line that is perpendicular to the lines whose directions are [3, 2, -1] and [1, -3, 4] respectively.
[5,13,-11]
[-5,-13,-11]
[-5,13,11]
[5,13,11]
30s
• Q2
Find the equation of the parabola with vertical axis that passes through the point (0,2) and points of intersection of the parabolas x^2 + 2x + 3y + 4 = 0 and x^2 – 3x + y + 3 = 0.
x^2 – 8x – y + 2 = 0
y^2 – 8x – y – 3 = 0
y^2 – 8x – y + 2 = 0
x^2 – 8x – y – 3 = 0
30s
• Q3
Find the coordinates of the point where the segment joining the points (2, -2, 1) and (5, 1, -2) crosses the 2, - plane.
(3, 0, 1)
(0, 3, -1)
(3, -1, 0)
(3, 1, 0)
30s
• Q4
Find the volume of the pyramid formed in the first octant by the plane 6x + 10y + 5z – 30 = 0 and the coordinate planes.
15
12
13
14
30s
• Q5
Determine the radius of sphere whose equation is x2 + y2 + z2 - 2x + 8y + 16z + 65 = 0.
6
4
5
7
30s
• Q6
Find the volume of a cube having its two faces laid in the planes 2x - y + 2z–3 = 0 and 6x-3y + 6z+ 8 = 0.
4319/729
564/729
4913/729
546/729
30s
• Q7
The three points (1, -1, -3), (2,0, -1) and (a, b, 3) lie on straight line, find the values of a and b.
4,3
4,1
2,4
4,2
30s
• Q8
A trough has an elliptical cross-section which is 18 inches wide on top and 12 inches deep. If the water surface is 8in below the top, find the width of the water surface.
6 sq.rt of 5
6 sq.rt of 2
12 sq.rt of 5
12 sq.rt of 2
30s
• Q9
A parabolic cable has a span of 200 ft and a sag of 50 ft, the equation of the cable is,
x^2 = 40y
y^2 = 200x
y^2 = 40x
x^2 = 200y
30s
• Q10
Find the equation of the circle that passes through the vertex and the two ends of the latus rectum of the parabola y^2 = 8x.
x^2 + y^2 = 4x
x^2 + y^2 = 8x
x^2 + y^2 = 10x
x^2 + y^2 = 5x
30s
• Q11
The parabola y^2 = 4ax and the line x = p enclosed an area with the centroid at the focus of the parabola. Find p in terms of a.
5/3a
3/5a
2/5a
3/4a
30s
• Q12
The supporting cable of a suspension bridge hangs in the form of parabola from the top of 22m tall towers which are 150m horizontally apart. If the lowest point on the cable is 7m above the roadway, find the vertical distance in meters of the cable from the roadway at the point which is 15m from one of the supports.
16.6
10.2
12.7
9.6
30s
• Q13
An ellipse has its center at (0,0) with its axis horizontal. The distance between the vertices is 8 and its eccentricity is 0.5. Compute the length of the longest focal radius from point (2,3) on the curve.
6
5
3
4
30s
• Q14
Find the equation of the bisector of the pair of acute angles formed by the line 4x + 2y = 9 and 2x – y = 8.
8x – 25 = 0
y + 8x – 25 = 0
y - 8x – 25 = 0
y + 4x – 25 = 0
30s
• Q15
Find the equation of one of the medians of a triangle with vertices (0,0), (6,0) and (4,4).
x + 2y = 6
2x – 5y = 4
2x – y = 10
x + 10y = 4
30s

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