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= _____________________