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
