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ELEMENTS > MESL (YELLOW BOOK 4) > Flashcards

MESL (YELLOW BOOK 4) Flashcards

1
Q

In general quadratic equation, if the discriminant is zero, the curve is a figure that represent a/an

A

Parabola

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2
Q

Equations relating x and y that cannot readily be solved explicitly for y as a function of y. Such equations may nonetheless determine y as a function of x or vise versa, such function is called.

A

Implicit function

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3
Q

In polar coordinate system, the length of the ray segment from a fixed origin is known as____.

A

Radius vector

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4
Q

Given the equations 3x^2+2x-5y+7=0
. Determine the curve.

A

Parabola

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5
Q

If eccentricity is less than one, then the curve is

A

Ellipse

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6
Q

Of what quadrant is A, if sec A is positive and csc A is negative

A

IV

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7
Q

If the general equation of the conic section is
Ax^2+2Bxy+Cy^2+Ey+F=0
and B^2-4AC>0
Then the conic is a/an

A

Hyperbola

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8
Q

What type of conic has an equation of
Ax^2+2Bxy+Cy^2+Ey+F=0

A

Ellipse

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9
Q

4x^2-256=0 is the equation of a/an

A

Parabola

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10
Q

The graph of a r=a+bcosθ is a

A

Limacon

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11
Q

In an ellipse, a chord which contains a focus and is in line perpendicular to the major axis is called

A

Latus Rectum

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12
Q

If all the y-terms have even exponents, the curve is symmetric with respect to the _____.

A

X-axis

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13
Q

It can be defined as the set of all points in the plane the sum of whose distances from two fixed points is a constant.

A

Ellipse

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14
Q

If the equation is unchanged by the substitution of -x of x , its curve is symmetric with respect to the

A

y-axis

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15
Q

What type of the curve is generated by a point which moves in uniform circular motion about an axis, while travelling with a constant speed parallel to the axis?

A

Helix

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16
Q

What is the graph of the equation?
Ax^2+2Bxy+Cy^2+Ey+F=0

A

Ellipse

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17
Q

It represents the distance of a point from the y-axis

A

Abscissa

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18
Q

A line passing through the focus and perpendicular to the directrix of a parabola is called

A

Axis of parabola

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19
Q

Locus of points on a side which rolls along a fixed line.

A

Cycloid

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20
Q

What is the length of the latus rectum of the curve
x^2=20y

A

20

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21
Q

If the product of the slopes of any two straight lines is negative 1, one of these is said to be _____ to the other.

A

Perpendicular

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22
Q

What is the curve represented by the equation
r=aθ

A

Spiral of Archimedes

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23
Q

Is the locus of a point that moves in a plane so that the difference of the distances from two fixed points of the locus is constant.

A

Hyperbola

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24
Q

The semi-conjugate axis of the hyperbola
x^2/9-y^2/4=1

A

2

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25
Q

The length of the latus rectum of the parabola
y=4px^2is

A

1/4p

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26
Q

The tangent function is negative in what quadrants

A

II & IV

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27
Q

The Cartesian or rectangular coordinates system was the first introduces by

A

Descartes

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28
Q

Also known as the x-coordinate

A

Abscissa

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29
Q

The x-coordinate of a point is positive in what quadrants?

A

I and IV

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30
Q

The y-coordinate of a point is positive in what quadrants?

A

I & II

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31
Q

State the quadrants in which the coordinates (15, -2) lies

A

IV

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32
Q

The rectangular coordinate system used to represent complex number.

A

Argand diagram

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33
Q

A cartesian coordinate system in which the axes are not perpendicular

A

Oblique coordinate system

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34
Q

The angle of rotation about the origin if the positive x-axis into the point with rectangular coordinates (a,b), representing the complex number a+bi is called_____ of the complex number.
-amplitude
-argument
-phase angle
-ALL OF THE ABOVE

A

-ALL OF THE ABOVE

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35
Q

The rectangular coordinates system in space is divided into eight compartments called

A

Octants

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36
Q

The angle of inclination of a straight line is the angle it makes with the

A

Positive x-axis

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37
Q

The points where the curve crossed the coordinates axes are called as the ______ with the axes.

A

Intersections

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38
Q

A line which is perpendicular to the x-axis has slope equal to

A

Infinity

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39
Q

A horizontal line has a slope of

A

Zero

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40
Q

A line parallel to the y-axis at a directed distancesx_1 has the equation

A

x=x_1

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41
Q

Let m1 and m2 be the respective slopes of the two perpendicular lines. Then

A

m1m2=-1

42
Q

If all the y-terms have even exponents, the curve is symmetric with respect to the

A

x-axis

43
Q

If the equation is unchanged by the substitution of -x for x and -y for y simultaneously, its curve is symmetric with respect to the

A

Origin

44
Q

If all of the terms of an equation have even odd exponents, the curve is symmetric with respect to the.

A

Origin

45
Q

If two linear equations, the x-coefficient of the first is equal to the y-coefficient of the send and the y-coefficient of the first is numerically equal but of opposite sign to the x-coefficient of the second, or vice versa, the lines represented are

A

Perpendicular to each other

46
Q

A cubic equation has either three real roots or one real root and two conjugate imaginary roots. The real roots are the points of intersection with

A

the y-axis

47
Q

If two equations have the same line as their graph, the equations are said to be

A

Dependent

48
Q

The points (a,1), (b,2), (c,3) are collinear. Which of the following is TRUE?
—- c-b=c-a
—- c-b=b-a
—- c-a=a-b
—- c-a=b-a

A

—- c-b=b-a

49
Q

In a linear equation Ax +By +C=0 if B=0 , then the equation has the form of x= -C/A

A

parallel to the y-axis

50
Q

The straight lines 4x-y+3=0&
8x-2y+6=0 are

A

are coincident

51
Q

Which of the following is the intercept form of an equation for straight lines?
Y= mx+b
(x/a) + (y/b)=1
y-y1=m(x-x1)
(x-a)+(y-b)=1

A

(x/a) + (y/b)=1

52
Q

A straight line where the curve approaches more and more closely but never touches it except at a limiting point of infinity.

A

Asymptotes

53
Q

Who coined the word “asymptote”?

A

Thomas Hobbes

54
Q

The path of a point which moves according to a given law or equation.

A

Locus

55
Q

The curve traced by a point moving in a plane is shown as the ____ of the point.

A

Locus

56
Q

A conic section is curve which is the intersection of

A

a cone and a plane

57
Q

When the ellipse approaches a circle as a limiting shape, its eccentricity approaches

A

0

58
Q

The set of points in a plane, the sum of whose distances from a fixed points is a constant, is

A

circle

59
Q

If a right circular cone is cut by a plane parallel to its base, it would reveal a/an

A

circle

60
Q

A _______ to a circle is a line that has exactly one point in common with the circle.

A

Tangent

61
Q

A conic section whose eccentricity is always less than 1.

A

Ellipse

62
Q

A locus of a point which moves so that the sum of the distances from two fixed points (foci) is constant and is equal to the length of the major axis.

A

Ellipse

63
Q

If the distance from the center to the focus of an ellipse is c, from the center to the vertex is a and from the center to the directrix is d, its eccentricity is

A

c/a

64
Q

A locus of a point which move so that it is always equidistant from a fixed point (focus) and from a fixed straight line (directrix).

A

Parabola

65
Q

The angle between the tangents at the end points of the latus rectum of a parabola is

A

90°

66
Q

The tangents to the parabola at the end point of its latus rectum intersect.

A

At the directrix

67
Q

In general equation of a conic section Ax^2+Bxy+Cy^2+Dx+Ey+F=0, if A and C have different signs, then the curve is a/an

A

Hyperbola

68
Q

If the discriminant of a quadratic equation is greater than zero, the graph is a/an

A

Hyperbola

69
Q

A chord passing through the focus of a parabola and perpendicular to the axis of symmetry.

A

Latus Rectum

70
Q

The latus rectum of the parabola x^2=4ay is

A

4a

71
Q

If a and b are lengths of semi-major and semi-minor axis of an ellipse respectively, then what is the length of its latus rectum?

A

2b^2/a

72
Q

The eccentricity of a regular hyperbola is

A

√2

73
Q

A parabola has an eccentricity

A

equal to 1

74
Q

The axis of the parabola that passes through the foci, vertices and center is called

A

transverse axis

75
Q

The locus of a moving point in a plane so that the difference of its distance from two fixed points (foci) is constant.

A

Hyperbola

76
Q

What is the term given to a circle with radius equal to half the transverse axis of the hyperbola or major axis of an ellipse and its center is the center of the conics?

A

Auxiliary Circle

77
Q

Which of the following is not a central conic?
Circle
Parabola
Ellipse
Hyperbola

A

Parabola

78
Q

Confocal conics are conics

A

Having the same foci

79
Q

Which of the following is NOT true?
A confocal ellipse and hyperbola always intersect at right angle
A prime number is not a composite number
A cosecant curve is a periodic function of period 360°
A conjecture is an axiom

A

A conjecture is an axiom

80
Q

If an ellipse and hyperbola have the same foci, they are said to be

A

Confocal conics

81
Q

The parabola y = -x2 + x + 1 opens

A

Downward

82
Q

A line segment joining two of its points and passing through a focus of a conic.

A

Focal chord

83
Q

Given the polar equation r = 3/(1 + 3cosθ)

A

Hyperbola

84
Q

The equation r = 4cosθ is a/an

A

Circle

85
Q

In polar coordinates system, the distance of any point P from the origin is called

A

Radius Vector

86
Q

The plane curve traced out by a fix point on the circle as the circle rolls along a line.

A

Cycloid

87
Q

A plane curve traced by a fixed point on a circle as it rolls along outside of a fixed circle

A

Epicycloid

88
Q

A plane curved traced by a fixed point on a circle as it rolls along the inside of a fixed circle

A

Hypocycloid

89
Q

The equation x3 + y3 – 3axy = 0 represents a

A

Folium of Descartes

90
Q

Continuous curve traced by a point moving around fixed point in same plane are steadily increasing or decreasing distance

A

Spiral

91
Q

Curve which is locus of centers of curvature of another curve envelope of all its normal.

A

Evolute

92
Q

Locus of the ultimate intersections or curves in a system of curves

A

Envelope

93
Q

Curve formed by uniform chain hanging freely from two points

A

Catenary

94
Q

The locus of a point such that its radius vector is proportional to its vectorial angle.

A

Spiral of Archimedes

95
Q

The graph of the equation r = a cos2θ is a

A

Rosette

96
Q

The locus of a point which rolls on a straight line
(x-axis)

A

Trochoid

97
Q

The equation r = a (1 + cosθ) is a polar equation of

A

Cardioids

98
Q

The equation r2 = a2cosθ is a

A

Lemniscates

99
Q

The equation r = a cosθ is a

A

Rosette

100
Q

The equation r = a θ is a

A

Spiral

ELEMENTS (7 decks)

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