Math Vocab Test Ch 9.5-10

parabola; directrix; focus

A _____ is defined as the set of all points (x,y) in a plane that are equidistant from a fixed line, called the _____, and a fixed point, called the _____, not on the line

conic

A _____ is the intersection of a plane and a double-napped cone

hyperbola; foci

A _____ is the set of all points (x,y) in a plane, the difference of whose distances from two distinct fixed points, called _____, is a positive constant

locus

A collection of points satisfying a geometric property can also be referred to as a _____ of points

tangent

A line is _____ to a parabola at a point on the parabola if the line intersects, but does not cross, the parabola at the point

focal chord

A line segment that passes through the focus of a parabola and has endpoints on the parabola is called a _____ _____

finite

A sequence is a _____ sequence if the domain of the function consists of the first n positive integers

arithmetic

A sequence is an _____ sequence if the first differences are all the same nonzero number

geometric; common

A sequence is called a _____ sequence if the ratios between consecutive terms are the same. This ratio is called the _____ ratio

arithmetic; common

A sequence is called an _____ sequence if the differences between two consecutive terms are the same. This difference is called the _____ difference

A'(x')^2+C'(y')^2+D'x'+E'y'+F'=0

After rotating the coordinate axis through an angle theta, the general second-degree equation in the new x'y'-plane will have the form _____

infinite sequence

An _____ _____ is a function whose domain is the set of positive integers

ellipse; foci

An _____ is the set of all points (x,y) in a plane, the sum of whose distances from two distinct fixed points, called _____, is constant

vertical; right

An equation of the form r=ep/1+ecos(theta) has a _____ directrix to the _____ of the pole

asymptotes

Each hyperbola has two _____ that intersect at the center of the hyperbola

directed distance; directed angle

For the point (r,theta), r is the _____ _____ from O to P and theta is the _____ _____ counterclockwise from the polar axis to the line segment OP

tan(theta)

If a nonvertical line has inclination theta and slope m, then m=_____

plane curve; parametric; parameter

If f and g are continuous functions of t on an interval I, the set of ordered pairs (f(t),g(t)) is a _____ _____ C. The equations x=f(t) and y=g(t) are _____ equations for C, and t is the _____

factorial

If n is a positive integer, n _____ is defined as n! = 1*2*3*4*...*(n-1)*n

second

If the _____ differences of a sequence are all the same nonzero number, then the sequence has a perfect quadratic model

| m(2)-m(1)/1+m(1)m(2)|

If two nonperpendicular lines have slope m(1) and m(2), the angle between the two lines is tan theta=_____

recursively

If you are given one or more of the first few terms of a sequence, and all other terms of the sequence are defined using previous terms, then the sequence is said to be defined _____

invariant under rotation

Quantities that are equal in both original equations of a conic and the equation of the rotated conic are _____ _____ _____

nth partial sum

The _____ _____ _____ of a sequence is the sum of the first n terms of the sequence

first

The _____ differences of a sequence are found by subtracting consecutive terms

orientation

The _____ of a curve is the direction in which the curve is traced out for increasing values of the parameter

inclination

The _____ of a nonhorizontal line is the positive angle theta (less than pi) measured counterclockwise from the x-axis to the line

vertex

The _____ of a parabola is the midpoint between the focus and the directrix

major axis; center

The chord joining the verticies of an ellipse is called the _____ _____, and its midpoint is the _____ of the ellipse

minor axis

The chord perpendicular to the major axis at the center of the ellipse is called the _____ _____ of the ellipse

binomial coefficients

The coefficients of a binomial expansion are called _____ _____

eccentricity

The concept of _____ is used to measure the ovalness of an ellipse

eccentricity; e

The constant ratio is the _____ of the conic and is denoted by _____

|Ax(1)+By(1)+C/ sir A^2+B^2|

The distance between the point (x1, y1) and the line Ax+By+C=0 is given by d=_____

cardioid

The equation r=1+sin(theta) represents a _____

convex limacon

The equation r=2+cos(theta) represents a _____ _____

circle

The equation r=2cos(theta) represents a _____

lemniscate

The equation r^2=4sin2(theta) represents a _____

mathematical induction

The first step in proving a formula by _____ _____ is to show that the formula is true when n=1

s(n)=a1(1-r^n/1-r)

The formula for the sum of a finite geometric sequence is given by _____

s=a1/1-r

The formula for the sum of an infinite geometric series is given by _____

sum of a finite arithmetic sequence

The formula s(n) = n/2(a(1)+a(n)) can be used to find the sum of the first n terms of an arithmetic sequence, called the _____ of a _____ _____ _____

terms

The function values a(1), a(2), a(3), a(4)... are called _____ of a sequence

Ax^2+Cy^2+Dx+Ey+F=0

The general form of the equation of a conic is given by ______

branches

The graph of a hyperbola has two disconnected parts called _____

theta=pi/2

The graph of r=f(sin theta) is symmetric with respect to the line _____

polar axis

The graph of r=g(cos theta) is symmetric with respect to the _____ _____

transverse axis; center

The line segment connecting the vertices of a hyperbola is called _____ ____, and the midpoint of the line segment is the _____ of the hyperbola

axis

The line that passes through the focus and vertex of a parabola is called the _____ of the parabola

conic

The locus of a point in the plane that moves so that its distance from a fixed point (focus) is in a constant ratio to its distance from a fixed line (directrix) is a _____

(n); nCr (r)

The notation used to denote a binomial coefficient is _____ or _____

summation notation

The notation used to represent the sum of the terms of a finite sequence is _____ _____ or sigma notation

a(n)=a1r^n-1

The nth term of a geometric sequence has the form _____

a(n)=dn+c

The nth term of an arithmetic sequence has the form _____

pole

The origin of the polar coordinate system is called the _____

polar

The plot the point (r,theta), use the _____ coordinate system

x=rcos(theta) y=rsin(theta) tan(theta)=y/x r^2=x^2+y^2

The polar coordinates (r,theta) are related to the rectangular coordinates (x,y) as follows: x=_____ y=_____ tan(theta)=_____ r^2=_____

rotation of axes

The procedure used to eliminate the xy-term in a general second-degree equation is called _____ of _____

eliminating the parameter

The process of converting a set of parametric equations to a corresponding rectangular equation is called _____ the _____

discriminant

The quantities B^2-4AC is called the _____ of the equation Ax^2+Bxy+Cy^2+Dx+Ey+F=0

series

The sum of the terms of a finite or infinite sequence is called a _____

geometric series

The sum of the terms of an infinite geometric sequence is called a _____ _____

binomial theorem; pascal's triangle

To find binomial coefficients, you can use the _____ _____ or _____ _____

expanding a binomial

When you write out the coefficients for a binomial that is raised to a power, you are _____ a _____

ellipse

e<1 is a _____ conic

parabola

e=1 is a _____ conic

hyperbola

e>1 is a _____ conic

index; upper; lower

for the sum, i is called the _____ of the summation, n is called the _____ limit of summation, and 1 is the _____ limit of summation