MESL (YELLOW BOOK 4) Flashcards
In general quadratic equation, if the discriminant is zero, the curve is a figure that represent a/an
Parabola
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.
Implicit function
In polar coordinate system, the length of the ray segment from a fixed origin is known as____.
Radius vector
Given the equations 3x^2+2x-5y+7=0
. Determine the curve.
Parabola
If eccentricity is less than one, then the curve is
Ellipse
Of what quadrant is A, if sec A is positive and csc A is negative
IV
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
Hyperbola
What type of conic has an equation of
Ax^2+2Bxy+Cy^2+Ey+F=0
Ellipse
4x^2-256=0 is the equation of a/an
Parabola
The graph of a r=a+bcosθ is a
Limacon
In an ellipse, a chord which contains a focus and is in line perpendicular to the major axis is called
Latus Rectum
If all the y-terms have even exponents, the curve is symmetric with respect to the _____.
X-axis
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.
Ellipse
If the equation is unchanged by the substitution of -x of x , its curve is symmetric with respect to the
y-axis
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?
Helix
What is the graph of the equation?
Ax^2+2Bxy+Cy^2+Ey+F=0
Ellipse
It represents the distance of a point from the y-axis
Abscissa
A line passing through the focus and perpendicular to the directrix of a parabola is called
Axis of parabola
Locus of points on a side which rolls along a fixed line.
Cycloid
What is the length of the latus rectum of the curve
x^2=20y
20
If the product of the slopes of any two straight lines is negative 1, one of these is said to be _____ to the other.
Perpendicular
What is the curve represented by the equation
r=aθ
Spiral of Archimedes
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.
Hyperbola
The semi-conjugate axis of the hyperbola
x^2/9-y^2/4=1
2
The length of the latus rectum of the parabola
y=4px^2is
1/4p
The tangent function is negative in what quadrants
II & IV
The Cartesian or rectangular coordinates system was the first introduces by
Descartes
Also known as the x-coordinate
Abscissa
The x-coordinate of a point is positive in what quadrants?
I and IV
The y-coordinate of a point is positive in what quadrants?
I & II
State the quadrants in which the coordinates (15, -2) lies
IV
The rectangular coordinate system used to represent complex number.
Argand diagram
A cartesian coordinate system in which the axes are not perpendicular
Oblique coordinate system
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
-ALL OF THE ABOVE
The rectangular coordinates system in space is divided into eight compartments called
Octants
The angle of inclination of a straight line is the angle it makes with the
Positive x-axis
The points where the curve crossed the coordinates axes are called as the ______ with the axes.
Intersections
A line which is perpendicular to the x-axis has slope equal to
Infinity
A horizontal line has a slope of
Zero
A line parallel to the y-axis at a directed distancesx_1 has the equation
x=x_1
Let m1 and m2 be the respective slopes of the two perpendicular lines. Then
m1m2=-1
If all the y-terms have even exponents, the curve is symmetric with respect to the
x-axis
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
Origin
If all of the terms of an equation have even odd exponents, the curve is symmetric with respect to the.
Origin
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
Perpendicular to each other
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
the y-axis
If two equations have the same line as their graph, the equations are said to be
Dependent
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
—- c-b=b-a
In a linear equation Ax +By +C=0 if B=0 , then the equation has the form of x= -C/A
parallel to the y-axis
The straight lines 4x-y+3=0&
8x-2y+6=0 are
are coincident
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
(x/a) + (y/b)=1
A straight line where the curve approaches more and more closely but never touches it except at a limiting point of infinity.
Asymptotes
Who coined the word “asymptote”?
Thomas Hobbes
The path of a point which moves according to a given law or equation.
Locus
The curve traced by a point moving in a plane is shown as the ____ of the point.
Locus
A conic section is curve which is the intersection of
a cone and a plane
When the ellipse approaches a circle as a limiting shape, its eccentricity approaches
0
The set of points in a plane, the sum of whose distances from a fixed points is a constant, is
circle
If a right circular cone is cut by a plane parallel to its base, it would reveal a/an
circle
A _______ to a circle is a line that has exactly one point in common with the circle.
Tangent
A conic section whose eccentricity is always less than 1.
Ellipse
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.
Ellipse
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
c/a
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).
Parabola
The angle between the tangents at the end points of the latus rectum of a parabola is
90°
The tangents to the parabola at the end point of its latus rectum intersect.
At the directrix
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
Hyperbola
If the discriminant of a quadratic equation is greater than zero, the graph is a/an
Hyperbola
A chord passing through the focus of a parabola and perpendicular to the axis of symmetry.
Latus Rectum
The latus rectum of the parabola x^2=4ay is
4a
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?
2b^2/a
The eccentricity of a regular hyperbola is
√2
A parabola has an eccentricity
equal to 1
The axis of the parabola that passes through the foci, vertices and center is called
transverse axis
The locus of a moving point in a plane so that the difference of its distance from two fixed points (foci) is constant.
Hyperbola
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?
Auxiliary Circle
Which of the following is not a central conic?
Circle
Parabola
Ellipse
Hyperbola
Parabola
Confocal conics are conics
Having the same foci
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 conjecture is an axiom
If an ellipse and hyperbola have the same foci, they are said to be
Confocal conics
The parabola y = -x2 + x + 1 opens
Downward
A line segment joining two of its points and passing through a focus of a conic.
Focal chord
Given the polar equation r = 3/(1 + 3cosθ)
Hyperbola
The equation r = 4cosθ is a/an
Circle
In polar coordinates system, the distance of any point P from the origin is called
Radius Vector
The plane curve traced out by a fix point on the circle as the circle rolls along a line.
Cycloid
A plane curve traced by a fixed point on a circle as it rolls along outside of a fixed circle
Epicycloid
A plane curved traced by a fixed point on a circle as it rolls along the inside of a fixed circle
Hypocycloid
The equation x3 + y3 – 3axy = 0 represents a
Folium of Descartes
Continuous curve traced by a point moving around fixed point in same plane are steadily increasing or decreasing distance
Spiral
Curve which is locus of centers of curvature of another curve envelope of all its normal.
Evolute
Locus of the ultimate intersections or curves in a system of curves
Envelope
Curve formed by uniform chain hanging freely from two points
Catenary
The locus of a point such that its radius vector is proportional to its vectorial angle.
Spiral of Archimedes
The graph of the equation r = a cos2θ is a
Rosette
The locus of a point which rolls on a straight line
(x-axis)
Trochoid
The equation r = a (1 + cosθ) is a polar equation of
Cardioids
The equation r2 = a2cosθ is a
Lemniscates
The equation r = a cosθ is a
Rosette
The equation r = a θ is a
Spiral
