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Worksheets2. Linear Equations, Vector Operations, TF, Coplanar, Conic, equ
Total questions: 151
Worksheet time: 2hrs 46mins
Solve the system of linear equations
No unique solution
no solution
notice the 0
x= 1; y= 2; z=3;
x=1; y=2 z=4
x=-2 y=1 z=-3
x=-2 y=4 z=1
x=-3 y=0 z=4
Solve the system of linear equations A = [5, 16; 3, 8] No unique solution
Solve the system of linear equations A = [2, 4; 1, 6]
No unique solution
idk
Solve the system of linear equations A = [0, 2; -1, 1] No unique solution
Solve the system of linear equations A = [0, 2; -1, 1] No unique solution
Solve the system of linear equations A = [0, 2; -1, 1] No unique solution
Solve the system of linear equations A = [0, 2; -1, 1] No unique solution
Solve the system of linear equations A = [0, 2; -1, 1] No unique solution
Solve the system of linear equations A = [0, 2; -1, 1] No unique solution
Solve the system of three linear equations (if the solution x=1,y=2,z=3, then write 1,2,3 without brackets and empty places): 6 = 2 + 3; 1 + 3 = 2 + 7; 3 = 2 + 1
(a)
Solve the system of three linear equations (if the solution x=1,y=2,z=3, then write 1,2,3 without brackets and empty places): -3 = 4 + 4; 4 = 2 + 3; 2 = 2 + 2
(a)
Solve the system of three linear equations (if the solution x=1,y=2,z=3, then write 1,2,3 without brackets and empty places): 3 = 2 + 5; 6 = 4 + 2; 12 = 3 + 2
(a)
Solve the system of three linear equations (if the solution x=1,y=2,z=3, then write 1,2,3 without brackets and empty places): -7 = 2 + 3; 1 = 3 + 2; 3 = 2 + 1
(a)
Solve the system of three linear equations (if the solution x=1,y=2,z=3, then write 1,2,3 without brackets and empty places): -2 = 4 + 4; 2 = 2 + 3; 3 = 2 + 2
(a)
Solve the system of three linear equations (if the solution x=1,y=2,z=3, then write 1,2,3 without brackets and empty places): -3 = 1 + 3; 2 = 3 + 2; 3 = 2 + 1
(a)
Solve the system of three linear equations (if the solution x=1,y=2,z=3, then write 1,2,3 without brackets and empty places): 4 = 1 + 5; 6 = 2 + 2; 3 = 2 + 1
(a)
Solve the system of three linear equations (if the solution x=1,y=2,z=3, then write 1,2,3 without brackets and empty places): 1 = 2 + 3; 2 = 3 + 2; 3 = 2 + 1
(a)
Solve the system of three linear equations (if the solution x=1,y=2,z=3, then write 1,2,3 without brackets and empty places): 11 = 2 + 3; 10 = 2 + 3; 14 = 3 + 2
(a)
Solve the system of three linear equations (if the solution x=1,y=2,z=3, then write 1,2,3 without brackets and empty places): 4 = -2 - 2; 1 = 2 + 2; 3 = 2 + 1
(a)
Solve the system of three linear equations (if the solution x=1,y=2,z=3, then write 1,2,3 without brackets and empty places): -5 = 0 - 2; 10 = 10 - 4; 6 = 4 - 3
(a)
Solve the system of three linear equations (if the solution x=1,y=2,z=3, then write 1,2,3 without brackets and empty places):
Solve the system of three linear equations (if the solution x=1,y=2,z=3, then write 1,2,3 without brackets and empty places):
Solve the system of three linear equations (if the solution x=1,y=2,z=3, then write 1,2,3 without brackets and empty places):
Solve the system of three linear equations (if the solution x=1,y=2,z=3, then write 1,2,3 without brackets and empty places):
Let a=(1,2,3),b=(0,-1,2). Find 2a-b.
(2,5,-1)
(2,4,5)
(2,5,4)
(2,-1,4)
(4,5,2)
Let a=(1,2,3),b=(0,-1,2). Find 2a+2b.
(2,5,-1)
(2,2,-10)
(2,2,10)
(-2,-1,4)
(4,10,2)
Let a=(1,2,3),b=(0,-1,2). Find a-3b.
(1,5,-1)
(-1,2,-10)
(1,5,-3)
(-1,-1,4)
(4,1,2)
Let a=(1,2,3),b=(0,-1,2). Find (1/2)a-4b.
(1/2,5,11/2)
(-1/2,2,-13)
(1/2,5,-13/2)
(-1,-1,4)
(3/2,1,2)
Let a=(1,2,4),b=(0,-1,2). Find 3a+b.
(3,5,-13/2)
(-3,2,-13)
(3,5,14)
(-1,-1,4)
(3/2,1,2)
Scalar or dot product of a=(1,2,3),b=(0,-1,2) is
11
5
4
7
6
Scalar or dot product of a=(-1,-2,3),b=(0,-1,2) is
11
4
8
7
6
Scalar or dot product of a=(1,-2,-3),b=(0,-1,2) is
(0,2,-6)
-3
-4
7
(1,2,-6)
Scalar or dot product of a=(1,5,-3),b=(1,-1,2) is
11
(1,-5,-6)
-10
7
(-1,5,6)
Scalar or dot product of a=(1,5,0),b=(1,-1,2) is
11
(1,-5,-6)
-4
7
(-1,5,6)
Scalar or dot product of a=(1,0,-3),b=(1,-1,2) is
3
(1,0,-6)
-5
-6
(-1,5,6)
Find the cross product of a=(1,-2,-3) and b=(0,-1,2)
(-7,2,-1)
-4
(-7,-2,-1)
-3
(-1,2,-1)
Find the cross product of a=(4,1,-3) and b=(0,-1,2)
(-1,8,-4)
-7
(-1,-8,-4)
-3
(0,-1,-6)
Find the cross product of a=(1,-2,4) and b=(5,-2,1)
(6,-19,8)
13
(6,19,8)
3
(5,4,4)
Find the area of a triangle formed by vectors a=(-1,2,-2) and b=(2,1,-1).
5√2
√50
5√2/2
5
√2
Find the area of a triangle formed by vectors a=(3,3,0) and b=(0,0,2).
6√2
√72
3√2
3
√2
Find the area of a parallelogram formed by vectors a=(1,2,1) and b=(3,0,3).
3√2
1/2√72
6√2
3
√2
Find the triple (or mix) product of vectors a=(1,-2,4), b=(5,-2,1), c=(1,2,0).
38
40
44
36
42
Find the triple (or mix) product of vectors a=(-1,-2,1), b=(5,-2,1), c=(1,2,0).
-8
10
12
6
4
Find the triple (or mix) product of vectors a=(-1,-2,1), b=(0,-2,3), c=(1,2,0).
4
1
2
6
-2
Find the volume of a pyramid constructed on vectors a=(1,2,1), b=(3,0,3), c=(2,0,-1).
0
36
3
6
18
Find the volume of a pyramid constructed on vectors a=(0,3,4), b=(3,0,3), c=(2,0,-1).
6
27
9/2
9
27/2
Find the volume of a parallelepiped constructed on vectors a=(0,-1,4), b=(3,0,3), c=(2,0,-1).
6
27
9
9/2
27/2
Simplify i×(j+k).
j
k
k-j
k+j
i
Simplify -j×(i+k).
k+i
k
k-i
j
k-j
Simplify k×(i+j+k).
j+k
i-k
j-i
j+k
j
Simplify i×(2j-k).
j
2k
2k+j
k+j
2k-j
Simplify -j×(i-2k).
k-2i
2k+i
k+2i
j
k-j
Simplify k×(i+j+k).
j+k
i−k
j−i
j+i
j
Simplify i×(2j−k).
j
2k
2k+j
k+j
2k−j
Simplify −j×(i−2k).
k−2i
2k+i
k+2i
j
k−j
Simplify k×(i−2k).
j+k
i−k
j
j+i
j−i
Let a=(1,0,4), b=(0,−4,5). Find 3a−b.
(3,4,−7)
(7,4,3)
(3,−4,9)
(1,−4,−1)
(3,4,7)
Let a=(3,2,−1), b=(9,7,0). Find 2a+b.
(15,11,−2)
(15,−11,2)
(12,9,−1)
(15,−5,−1)
(12,−3,−2)
Let a=(5,−1,0), b=(3,4,2). Find a+2b.
(8,3,2)
(2,−5,−2)
(11,7,4)
(−11,−4,2)
(−1,5,2)
Let a=(−9,2,−1), b=(−3,4,2). Find a−3b.
(0,10,7)
(−6,−2,−3)
(−6,2,−3)
(0,−10,−7)
(−18,6,−3)
Let a=(4,3,1), b=(2,8,0). Find 2a−b.
(2,−5,1)
(6,11,1)
(10,14,2)
(−6,2,−2)
(6,−2,2)
Scalar or dot product of a=(7,9,10), b=(1,0,3) is.
27
37
7
−37
−17
Scalar or dot product of a=(5,6,5), b=(4,2,3) is.
43
37
13
47
25
Scalar or dot product of a=(−3,4,1), b=(0,2,0) is.
4
5
9
18
8
Scalar or dot product of a=(−1,0,4), b=(3,2,1) is.
1
11
−1
21
13
Scalar or dot product of a=(9,6,1), b=(4,2,−7) is.
11
55
41
37
14
Scalar or dot product of a=(2,3,0), b=(0,4,1) is.
11
22
2
21
12
Find the cross product of a=(7,2,1) and b=(5,3,0).
(−3,5,11)
41
(−3,−5,7)
42
(5,−3,11)
Find the cross product of a=(4,0,2) and b=(3,−1,4).
(−2,10,4)
20
(10,−2,−4)
19
(2,−10,−4)
Find the cross product of a=(2,3,1) and b=(4,6,7).
(−10,15,0)
33
(15,−10,0)
23
(8,18,7)
Find the cross product of a=(5,6,10) and b=(−1,0,2).
(−12,20,−3)
(12,−20,6)
15
(20,−12,4)
(−5,0,20)
Find the area of a triangle formed by vectors a=(3,−3,6) and b=(2,1,4).
√74
√5
9√5/2
9√5
19√5/2
Find the area of a triangle formed by vectors a=(−1,3,1) and b=(2,−5,1).
6√4
√74
3√2
3
√74/2
Find the area of a parallelogram formed by vectors a=(−1,2,4) and b=(2,0,3).
√173/2
√173
21
7√3
√153/4
Find the area of a parallelogram formed by vectors a=(5,2,0) and b=(−2,1,3).
4√38
√332
8√4
3√38
√342/2
Find the triple (or mix) product of vectors a=(5,3,1), b=(4,0,2), c=(3,1,−5).
42
72
12
48
−36
Find the triple (or mix) product of vectors a=(4,2,0), b=(−10,3,1), c=(4,2,7).
124
24
−220
224
−112
Determine the cosine of the angle between a =(3,-4,-1) and b=(0,5,2).
22/26
29/−
20/21
27/−
There no correct answer.
Determine the projection of b=(2,1,-1) and a =(1,0,-2).
48( , 0, )55−
(1, 0, 2)−(−∞,−4]∪[−3,+∞)
4/5−[−3,+∞)
4(1, 0, 2)5−
There no correct answer.
Find the scalar (or dot) product of vectors u=(2, 3), v=(5, -7).
(a)
Suppose that u * (v x w )=3. Find (u x w) * v.
(a)
Find |U x V|. U =(1, -5, 4), V=(3, 3, 3).
(a)
Are the planes 4x – y + 2z = 5 and 7x – 3y + 4z =8 parallel?
No
Yes(−∞,−4]∪[−3,+∞)
Are the planes x – 4y – 3z -2 = 0 and 3x – 12y – 9z – 7 = 0 parallel?
No
Yes(−∞,−4]∪[−3,+∞)
Which of the vectors a=(1,2), b=(−1,2), c=(4,8) are collinear?
a and b
b and c
a and c
None of them
a,b,c
Which of the vectors a=(−1,2), b=(1,−2), c=(4,8) are collinear?
a and b
b and c
a and c
None of them
a,b,c
Which of the vectors a=(1,3), b=(−1,2), c=(4,8) are collinear?
a and b
b and c
a and c
None of them
a,b,c
Find the value of n where the vectors a=(2,4), b=(n,1) are perpendicular.
2
1
−2
−4
0
=(4,8) are collinear?
a⃗andb⃗
b⃗andc⃗
a⃗andc⃗
None of them
a⃗,b⃗,c⃗
Find the value of n where the vectors a⃗=(2,4),b⃗=(n,1) are perpendicular.
2
1
-2
-4
0
Find the value of n where the vectors a⃗=(2,4,1),b⃗=(n,1,-8) are perpendicular.
-2
1
2
-4
0
Which of the vectors a⃗=(-1,3),b⃗=(2,1),c⃗=(-4,8) are perpendicular?
a⃗andb⃗
b⃗andc⃗
a⃗andc⃗
None of them
a⃗,b⃗,c⃗
Calculate the value of a for the points (a, 0, 1), (0, 1, 2), (1, 2, 3) and (7, 2, 1) so that they are coplanar.
a = 2
a = 1
a = -2
a = -1
Calculate the value of x for the coplanar set of points A = (0, 0, 1), B = (0, 1, 2), C = (-2, 1, 3) and D = (x, x−1, 2).
x = 3
x = 1
x = -3
x = 4
Which of the following statements are true?
The three vectors are coplanar, if their triple product is zero
The three vectors are coplanar, if their triple product is not equal to zero
Vectors are coplanar if among them more than two linearly independent vectors
The three vectors are coplanar if they are linearly independent
The three vectors are coplanar, if dot product of two of them not equal to zero
Which of the following statements are true?
The three vectors are coplanar, if they are linearly dependent
The three vectors are coplanar, if their triple product is not equal to zero
Vectors are coplanar if among them more than two linearly independent vectors
The three vectors are coplanar if they are linearly independent
The three vectors are coplanar, if dot product of two of them not equal to zero
Which of the following statements are true?
Two vectors are collinear if the relations of their coordinates are equal
Vectors are collinear if the mixed product is equal to one
Vectors are collinear if the mixed product is equal to zero
Vectors are collinear if the cross product is not equal to zero vector
Two vectors are collinear if there is no relation of their coordinates
Which of the following statements are true?
Two vectors are collinear if there exists some number n such that a = n*b
Vectors are collinear if the mixed product is equal to one
Vectors are collinear if the mixed product is equal to zero
Vectors are collinear if the cross product is not equal to zero vector
Two vectors are collinear if there is no relation of their coordinates
Which of the following statements are true?
Vectors are collinear if their cross product is equal to the zero vector
Vectors are collinear if the mixed product is equal to one
Vectors are collinear if the mixed product is equal to zero
Vectors are collinear if the cross product is not equal to zero vector
Two vectors are collinear if there is no relation of their coordinates
Find undefined expressions (2 correct answers)
-50%
50%
-50%
50%
Find coplanar vectors. (2 correct answers)
50%a = 2i + 3j+ k, b = i - j, c = 7i + 3j + 2k
50%a = (1, 2, -1), b = (2, 4, -2), c = (1, 1, -3)
-50%a = i + 3j+ k, b = i - j, c = 6i + 3j + 2k
-50%a = (1, -3 , 1), b = (2, -3, 5), c = (1, -1, 2)
For the following vectors find right answers. (2 correct answers) u = (1, 3, −1), v = (3, 7, −7), w = (1, 2, −3)
Linearly dependent vectors
Linearly independent vectors
Basis vectors
Coplanar vectors
For the following vectors find right answers. (2 correct answers) u = (1, 4, 5), v = (1, 1, 0), w = (3, 6, 8)
Linearly dependent vectors
Linearly independent vectors
Basis vectors
Coplanar vectors
For the following vectors find right answers. (2 correct answers) u = (1, 3, −1), v = (3, 7, −7), w = (1, 2, −3)
Linearly dependent vectors
Linearly independent vectors
Basis vectors
Coplanar vectors
For the following vectors find right answers. (2 correct answers) u = (1, 4, 5), v = (1, 1, 0), w = (3, 6, 8)
Linearly dependent vectors
Linearly independent vectors
Basis vectors
Coplanar vectors
For the following vectors find right answers. (2 correct answers) u = (1, 4, 5), v = (1, 1, 0), w = (3, 6, 8)
Linearly dependent vectors
Linearly independent vectors
Basis vectors
Coplanar vectors
For the following vectors find right answers. (2 correct answers) u = (1, 3, −1), v = (3, 7, −7), w = (1, 2, −3)
Linearly dependent vectors
Linearly independent vectors
Basis vectors
Coplanar vectors
The eccentricity of a conic section is 1. The conic section must be:
An ellipse
A hyperbola
A circle
A parabola
The eccentricity of a conic section is 1,5. The conic section must be:
An ellipse
A hyperbola
A circle
A parabola
The eccentricity of a conic section is 0,4. The conic section must be:
An ellipse
A hyperbola
A circle
A parabola
The eccentricity of a conic section is 0. The conic section must be:
An ellipse
A hyperbola
A circle
A parabola
Write an equation for the ellipse with each set of characteristics. Vertices (4; 3), (4; -9); length of minor axis is 8
(1/36)(x^2) + (1/16)(y^2) = 1
(1/16)(x^2) + (1/36)(y^2) = 1
(1/36)(x^2) + (1/16)(y^2) = 2
(1/16)(x^2) + (1/36)(y^2) = 2
Write an equation for the ellipse with each set of characteristics. foci (-6; 9), (-6; -3); length of major axis is 20
(1/100)(x^2) + (1/64)(y^2) = 1
(1/16)(x^2) + (1/64)(y^2) = 1
(1/64)(x^2) + (1/100)(y^2) = 1
(1/100)(x^2) + (1/36)(y^2) = 1
Write an equation for the ellipse with each set of characteristics. Co-vertices (-13; 7), (-3; 7); length of major axis is 16
(1/64)(x^2) + (1/25)(y^2) = 1
(1/25)(x^2) + (1/64)(y^2) = 1
(1/64)(y^2) + (1/100)(x^2) = 1
(1/100)(y^2) + (1/36)(x^2) = 1
Write an equation for the ellipse with each set of characteristics. foci (-10; 8), (14; 8); length of major axis is 30
(1/81)(x^2) + (1/225)(y^2) = 1
(1/225)(x^2) + (1/64)(y^2) = 1
(1/64)(y^2) + (1/225)(x^2) = 1
(1/100)(y^2) + (1/81)(x^2) = 1
Write an equation for a circle that satisfies each set of conditions. Center at (-1; 7) and diameter 6
(x + 1)^2 + (y - 7)^2 = 9
(x - 0.5)^2 + (y - 0.5)^2 = 9
(x - 0.5)^2 + (y + 0.5)^2 = 9
(x - 0.5)^2 + (y + 0.5)^2 = 36
Write an equation for a circle that satisfies each set of conditions. Center at (2; 0), endpoints of diameter at (-5; 0) and (9;0)
(x - 2)^2 + (y - 0)^2 = 49
(x - 0)^2 + (y - 0)^2 = 9
(x - 0)^2 + (y - 0)^2 = 81
(x - 5)^2 + (y - 0)^2 = 25
Write the standard form of the equation for each ellipse. The vertices are at (-10; 0) and (10; 0), and the eccentricity e is 3/5.
(1/100)(x^2) + (1/64)(y^2) = 1
(1/100)(y^2) + (1/64)(x^2) = 1
(1/100)(x^2) + (1/64)(y^2) = 2
(1/25)(y^2) + (1/10)(x^2) = 1
Write the standard form of the equation for each ellipse. The co-vertices are at (0; 1) and (6; 1), and the eccentricity e is 4/5.
(1/25)(x^2) + (1/9)(y^2) = 1
(1/9)(x^2) + (1/25)(y^2) = 1
(1/9)(y^2) + (1/25)(x^2) = 1
(1/9)(x^2) + (1/25)(y^2) = 2
Find the coordinates of points where a line intersects a circle, 9 + x = y, o (-2; 7) and (-5; 4), ● (-2; 7) and (-9; 0), o (-1; 8) and (2; 11), o (-3; 6) and (-5; 4)
(-2; 7) and (-5; 4)
(-2; 7) and (-9; 0)
(-1; 8) and (2; 11)
(-3; 6) and (-5; 4)
Find the coordinates of points where a line intersects a circle, 1 + x = y, o (-2; 3) and (-5; 6), ● (-2; 3) and (6; -5), o (-1; 2) and (2; -1), o (-3; 4) and (-5; 6)
(-2; 3) and (-5; 6)
(-2; 3) and (6; -5)
(-1; 2) and (2; -1)
(-3; 4) and (-5; 6)
Determine type of a curve represented by the equation 2x^2 + 3y^2 - 4x + 6y - 7 = 0.
parabola
hyperbola
ellipse
point
two parallel lines
Determine type of a curve represented by the equation x^2 - y^2 - 4x + 2y - 4 = 0.
parabola
hyperbola
ellipse
point
two parallel lines
Determine type of a curve represented by the equation x^2 - y^2 - 4x + 2y + 3 = 0.
parabola
hyperbola
ellipse
two perpendicular lines
point
Determine type of a curve represented by the equation x^2 + y^2 - 6x - 2y + 10 = 0.
parabola
hyperbola
ellipse
two perpendicular lines
point
Determine type of a curve represented by the equation x^2 - 6x - 2y + 10 = 0.
parabola
hyperbola
ellipse
point
two perpendicular lines
Find the center and radius of a circle x^2 + y^2 - 6x + 4y - 23 = 0.
center (3; −2) and radius is √10
center (3;2) and radius is √23
center (3;−2) and radius is 6
center (−3;2) and radius is 6
center (3;2) and radius is 36
Find the center and radius of a circle x^2 + y^2 + 5x - 7y + 5^2 = 0.
center(5/2; −7/2)and radius is √10
center(−5/2; 7/2) and radius is √32
center(−5/2; 7/2)and radius is 4
center(5/2; −7/2)and radius is 4
center(5/2; 7/2)and radius is 16
Find the center and radius of the circle x^2 + y^2 − 4x + 2y = −1.
center (1; −2) and radius is 2
center (−1;2) and radius is 4
center (2; −1) and radius is 2
center (−2;1) and radius is 4
center (−2;1) and radius is 2
Find the center and radius of the circle x^2 + y^2 + 4x − 4y = 0.
center (2; −2) and radius is 2√3
center (2; −2) and radius is 4
center (−2;2) and radius is 2√2
center (−2;2) and radius is 8
center (2;2) and radius is 2√3
Find the center and radius of the circle x^2 + y^2 + 4x = 0.
center (0; 2) and radius is 2
center (0; −2) and radius is 4
center (−2;0) and radius is 2
center (−2;0) and radius is 4
center (0;−2) and radius is 2
Find the canonical equation of an ellipse with parameters b=6, c=√28.
x^2/64 + y^2/36 = 1
x^2/36 + y^2/64 = 1
x^2/64 - y^2/36 = 1
x^2/36 - y^2/64 = 1
x^2/36 + y^2/64 = 0
Find the canonical equation of an ellipse with parameters b=2, c=4√2.
x^2/4 + y^2/36 = 1
x^2/36 + y^2/4 = 1
x^2/4 - y^2/36 = 1
x^2/36 - y^2/4 = 1
x^2/36 + y^2/4 = 0
Find the canonical equation of an ellipse with parameters a=4, c=3.
x^2/7 + y^2/16 = 1
x^2/16 + y^2/7 = 1
x^2/7 - y^2/16 = 1
x^2/16 - y^2/7 = 1
x^2/16 - y^2/7 = 0
Find the canonical equation of a hyperbola with parameters a=13, c/a=14/13.
x^2/27 + y^2/169 = 1
x^2/169 - y^2/27 = 1
x^2/27 - y^2/169 = 1
x^2/169 - y^2/27 = -1
x^2/13 - y^2/27 = 1
Find the canonical equation of a hyperbola with parameters b/a=3/4, c/a=5/4.
x^2/9 + y^2/16 = 1
x^2/16 - y^2/9 = 1
x^2/9 - y^2/16 = 1
x^2/16 - y^2/9 = -1
x^2/4 - y^2/3 = 1
Find the canonical equation of a hyperbola with parameters b=2√10, c=-11.
x^2/40 + y^2/81 = 1
x^2/81 - y^2/40 = 1
x^2/9 - y^2/16 = 1
x^2/40 - y^2/81 = -1
x^2/9 - y^2/3 = 1
Given the ellipse x^2/20 + y^2/5 = 1 and straight line y=x+3. This straight line intersects ellipse or not, if intersects then find the point of intersection?
Yes, at points (−1; −4) and (11/5; −4/5)
No
Yes, at points (−4; −1) and (−4/5; 11/5)
Yes, at points (−4; −1) and (−20; −17)
Yes, at points (−1; −4) and (−17; −20)
Given the ellipse x^2/4 + y^2/5 = 1 and straight line x=−2. This straight line intersects ellipse or not, if intersects then
Given the ellipse x^2/4 + y^2/5 =1 and straight line x=-2. This straight line intersects ellipse or not, if intersects then find the point of intersection?
Yes, at points (-2;0) and (2;0)
No
Yes, at point (-2;0)
Yes, at points (-2; -1) and (-2; -17)
Yes, at points (-2; -4) and (-2; 0)
Given the hyperbola x^2/9 - y^2/36 =1 and straight line y=-2x. This straight line intersects ellipse or not, if intersects then find the point of intersection?
Yes, at points (-3√2; 3√2) and (3√2; -3√2)
No
Yes, at points (3√2; -3√2) and (-3√2; 3√2)
Yes, at points (3√2; 3√2) and (-3√2; -3√2)
Yes, at points (3√2; 3√2) and (-3√2; -3√2)
Given the hyperbola x^2/9 - y^2/36 =1 and straight line x-1=0. This straight line intersects ellipse or not, if intersects then find the point of intersection?
Yes, at points (-3√2; 3√2) and (3√2; -3√2)
No
Yes, at points (3√2; -3√2) and (-3√2; 3√2)
Yes, at points (3√2; 3√2) and (-3√2; -3√2)
Yes, at points (3√2; 3√2) and (-3√2; -3√2)
Find the parameters a,b,c of ellipse represented by the equation 2x^2 + 3y^2 - 4x + 6y - 7=0.
a=6, b=4, c=10
a=6, b=4, c=2
a=√6, b=2, c=√2
a=√6, b=2, c=√10
a=√6, b=4, c=12
Find the parameters a,b,c of hyperbola represented by the equation 2x^2 - 3y^2 - 4x + 6y - 7=0.
a=3, b=2, c=1
a=3, b=2, c=5
a=√3, b=√2, c=√5
a=√3, b=√2, c=1
a=√6, b=4, c=12
Write canonical equation of the parabola, if its focus is at F(3,0)
y^2 = 36x
y^2 = 12x
x^2 = 36y
x^2 = 12y
y^2 = -36x
What is the equation of the circle centred at (3,4) and radius is equal to 5?
22(3)(4)25xy− + − =
22(3)(4)25xy + + + =
22(3)(4)25xy + + − =
22(3)(4)25xy + − − =
22(3)(4)25xy − − − =
What is the equation of the circle catered at (-4,3) and radius is equal to 1?
5x^4 - 3x^2 + 7x^4 + 2x^3 + 1
22(4)(3)1xy + + − =
22(4)(3)1xy + + + =
22(4)(3)1xy − + + =
22(4)(3)1xy − + − =
What is the equation of the circle, passing through the points (-1, 1), (3, 9), (8, 4)?
22(3)(4)25xy− + − =
22(3)(4)25xy + + + =
22(3)(4)25xy + + − =
22(3)(4)25xy + − − =
22(3)(4)25xy − − − =
What is the y - intercept of the circle 22(2)(5)16xy− + + =?
(0, 5 2 3)−
(2 3, 0)
(0, 2 3)
(0, 1 2 3)−
(0, 2 2 3)
Determine the center and radius: 22(4)(4)8xy− + − =?
3 :(1,);:2 center radius r − =
3 :(1,);:4 center radius r − =
:(1, 3);:2 center radius r − =
