Math vocab chapter 9-10

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.

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.

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 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. The 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.

ellipse: foci

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

infinite sequence

An __________ __________ is a function whose domain is the set of positive integers.

vertical; right

An equation of the form r = ep / 1 + ecosθ 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,θ), r is the _______ _____ from O to P and θ is the ______ ______ counterclockwise from the polar axis to the line segment OP

Index, upper, lower

For the sum n sigma i=1 ai, i is called the __________ of summation, n is the __________ limit of summation, and 1 is the __________ limit of summation

tanθ

If a nonvertical line has inclination 0 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 ______ difference of a sequence are all the same nonzero number, then the sequence has a perfect quadratic model.

|((m2-m1)/(1+m1m2))|

If two nonperpendicular lines have slopes m1 and m2, the angel between the two lines is tanθ = ________

Recursively

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

(a) iii (b) i (c) ii

Match the conic with its eccentricity (a) e < 1 (b) e = 1 (c) e > 1 (i) parabola (ii) hyperbola (iii) ellipse

first

The ___ difference of a sequence of a sequence are found by subtracting consecutive terms

vertex

The ____ of a parabola is the midpoint between the focus and the directrix.

inclination

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

orientation

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

Nth partial sum

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

major axis: center

The chord joining the vertices 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 coefficents

The coefficients of a binomial expansion are called ____ _____

eccentricity

The concept of ____ is used to measure the ovalness of an ellipse.

|Ax1+By1+C|/sqrt(A^2+B^2)

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

cardiod

The equation r = 1 + sinθ represents a ________

circle

The equation r = 2cosθ represents a _______

lemniscate

The equation r^2 = 4sin2θrepresents a __________

mathematical induction

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

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

The formula for the sum of a finite geometric sequences 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 sn=(n/2)(a1+an) can be used to find the sum of the first n terms of an arithmetic sequence, called the __________

Terms

The function vaules a1, a2, a3, a4,.... are called the __________ 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 ______.

convex limacon

The graph of r = 2 + cosθ represents a ______ _______

θ= pi/2

The graph of r = f(sinθ) is symmetric with respect to the line __________________

polar axis

The graph of r = g(cosθ) is symmetric with respect to the ___________ ____________

transverse axis: center

The line segment connecting the vertices of a hyperbola is called the ______ ______, 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 over r), nCr

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

an = a1r^n-1

The nth term of a geometric sequence has the form ______

An= Dn+c

The nth term of an arithmetic sequence has the form __________

pole

The origin of the polar coordinate system is called the _____

eliminating the parameter

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

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 _____ _____

polar

To plot the point (r, θ) use the ________ coordinate system

expanding a binomial

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

eccentricity: e

the constant ratio is the ______ of the conic and is denoted by ________

x = rcosθ tanθ=y/x y =rsinθ r^2 = x^2 + y^2

the polar coordinates (r,0) are related to the rectangular coordinates (x,y) as follows: x = __________________ tan 0 = _________________ y = __________________ r^2= _____________________