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Q 1/30
Score 0
Find the direction of the line that is perpendicular to the lines whose directions are [3, 2, -1] and [1, -3, 4] respectively.
30
[5,13,-11]
[-5,-13,-11]
[-5,13,11]
[5,13,11]
Q 2/30
Score 0
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 β 3x + y + 3 = 0.
30
x^2 β 8x β y + 2 = 0
y^2 β 8x β y β 3 = 0
y^2 β 8x β y + 2 = 0
x^2 β 8x β y β 3 = 0
30 questions
Q.
Find the direction of the line that is perpendicular to the lines whose directions are [3, 2, -1] and [1, -3, 4] respectively.
1
30 sec
Q.
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 β 3x + y + 3 = 0.
2
30 sec
Q.
Find the coordinates of the point where the segment joining the points (2, -2, 1) and (5, 1, -2) crosses the 2, - plane.
3
30 sec
Q.
Find the volume of the pyramid formed in the first octant by the plane 6x + 10y + 5z β 30 = 0 and the coordinate planes.
4
30 sec
Q.
Determine the radius of sphere whose equation is x2 + y2 + z2 - 2x + 8y + 16z + 65 = 0.
5
30 sec
Q.
Find the volume of a cube having its two faces laid in the planes 2x - y + 2zβ3 = 0 and 6x-3y + 6z+ 8 = 0.
6
30 sec
Q.
The three points (1, -1, -3), (2,0, -1) and (a, b, 3) lie on straight line, find the values of a and b.
7
30 sec
Q.
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.
8
30 sec
Q.
A parabolic cable has a span of 200 ft and a sag of 50 ft, the equation of the cable is,
9
30 sec
Q.
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.
10
30 sec
Q.
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.
11
30 sec
Q.
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.
12
30 sec
Q.
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.
13
30 sec
Q.
Find the equation of the bisector of the pair of acute angles formed by the line 4x + 2y = 9 and 2x β y = 8.
14
30 sec
Q.
Find the equation of one of the medians of a triangle with vertices (0,0), (6,0) and (4,4).
15
30 sec
Q.
Find the area bounded by the curve rΒ² = 4cos 2π.
16
30 sec
Q.
Find the area enclosed by r = 2 cos 3 theta.
17
30 sec
Q.
A parabola having its axis along the x-axis passes through (-3, 6). Compute the length of latus rectum if the vertex is at the origin.
18
30 sec
Q.
Classify the graph of the equation x^2 + xy + y^2 β 6 = 0
19
30 sec
Q.
What is the slope of the line through (-1, 2) and (4, -3)?
20
30 sec
Q.
If the line kx + 3y + 8 = 0 has a slope of 2/3, determine k.
21
30 sec
Q.
What is the area of the ellipse whose eccentricity is 0.60 and whose major axis has a length of 8?
22
30 sec
Q.
Calculate the eccentricity of an ellipse whose major axis and latus rectum has lengths of 10 and 32/5, respectively.
23
30 sec
Q.
Find the radius of the circle inscribed in the triangle determined by the line y = x + 4, y = -x β 4 and y = 2/7 x + 2.
24
30 sec
Q.
A chord passing through the focus of the parabola yΒ² = 8x has one end at the point (8, 8). Where is the other end of the court?
25
30 sec
Q.
Find the eccentricity of the ellipse when the length of its latus rectum is 2/3 of the length of its major axis.
26
30 sec
Q.
The coordinates of points A and B are A (-2, -3) and B (2, -5). What is an equation of the line that is perpendicular to AB at its midpoint?
27
30 sec
Q.
The arch of an underpass is a semi-ellipse 60 ft wide and 20 ft high. Find the clearance at the edge of a lane if the edge is 20 ft from the middle.
28
30 sec
Q.
If the distance between points A (2, 10, 4) and B (8, 3, z) is 9.434, what is the value of z?
29
30 sec
Q.
What is the height of the parabolic arch which has a span of 48 ft. and having a height of 20 ft. at a distance of 16 ft. from the center of the span?
