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Chapter 10
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Gravity
Terms in this set (38)
Chapter 10
Section 1
The __________ of a nonhorizontal line is the positive angle theta (less than pi) measured counterclockwise from the x-axis to the line.
Inclination
If a nonvertical line has inclination theta and slope m, then m = __________.
tan theta
If two nonperpendicular lines have slopes m1 and m2, then the angle between the two lines is tan theta = __________.
PAGE 692 # 2
The distance between the point (x1,y1) and the line Ax + By + C = 0 is given by d = __________.
PAGE 692 # 3
Chapter 10
Section 2
A __________ is the intersection of a plane and a double-napped cone.
Curve
When a plane passes through the vertex of a double-napped cone, the intersection is a __________ __________.
Degenerate conic
A collection of points satisfying a geometric property can also be referred to as a __________ of points.
Locus
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.
Parabola
Directrix
Focus
The line that passes through the focus and the vertex of a parabola is called the __________ of the parabola.
Axis
The __________ of a parabola is the midpoint between the focus and directrix.
Vertex
A line segment that passes through the focus of a parabola and has endpoints on the parabola is called a __________ __________.
Focal chord
A line is __________ to a parabola at a point on the parabola when the line intersects, but does not cross, the parabola at the point.
Tangent
Chapter 10
Section 3
An __________ is the set of all points (x,y) in a plane, the sum of whose distances from two distinct fixed points, called __________, is a constant.
Ellipse
Foci
The chord joining the vertices of an ellipse is called the __________ __________, and its midpoint is the __________ of the ellipse.
Major axis
Center
The concept of __________ is used to measure the ovalness of an ellipse.
Eccentricity
Chapter 10
Section 4
A __________ is the set of all points (x,y) in a plane for which the absolute value of the difference of the distances from two distinct fixed points, called __________, is constant.
Hyperbola
Foci
The graph of a hyperbola has two disconnected parts called __________.
Branches
The line segment connecting the vertices of a hyperbola is called the __________ __________, and the midpoint of the line segment is the __________ of the hyperbola.
Transverse axis
Center
Each hyperbola has two __________ that intersect at the center of the hyperbola.
Asymptotes
Chapter 10
Section 5
The procedure used to eliminate the xy-term in a general second-degree equation is called __________ of__________.
Rotation of axis
After rotating the coordinate axes through an angle theta, the general second-degree equation in the new x'y'-plane will have the form __________.
PAGE 729 Number 2
Quantities that are equal in both original equation of a conic and the equation of the rotated conic are __________ __________ __________.
Invariant under rotation
The quantity B squared - 4AC is called the __________ of the equation Ax sqaured + Bxy + Cy squared + Dx +Ey + F = 0
Discriminant
Chapter 10
Section 6
If f and g are continuous of t on an interval, theen the set of ordere pairs (f(t), g(t)) is a __________ __________ C.
Plane curve
The __________ of a curve is the direction in which the curve is traced out for increasing values of the parameter.
Orientation
The process of converting a set of parametric equations to a corresponding rectangular equation is called the __________ the __________.
Eliminating the parameter
A curve traced out by a point on the circumfrence of a circle as the circle rolls along a straight line in a plane is called a __________.
Cycloid
Chapter 10
Section 7
The origin of the polar coordinate system is called the __________.
Pole
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.
Directed distance
Directed angle
To plot the point (r, theta), use the __________ coordinate system.
Polar
The polar coordinates (r, theta) are related to the rectangular coordinates (x,y) as follows:
x = __________
y = __________
tan theta __________
r squared __________
x = r cos theta
y = r cos theta
tan theta = y/x
r squared = x squared + y squared
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