MESL (YELLOW BOOK 4) Flashcards by Romnick Jay Pagal

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

Parabola

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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

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

Radius vector

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

Parabola

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If eccentricity is less than one, then the curve is

Ellipse

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

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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

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

Ellipse

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

Parabola

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The graph of a r=a+bcosθ is a

Limacon

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

Latus Rectum

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

X-axis

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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

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

y-axis

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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

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

Ellipse

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

Abscissa

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

Axis of parabola

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

Cycloid

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

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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

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What is the curve represented by the equation
r=aθ

Spiral of Archimedes

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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

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

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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

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

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

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