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Chapter 10 Vocabulary - Precalculus (10.2, 10.3, 10.4 only)

                                    Name: ___________________
                                    Period: __________________
                                    Date: ____________________
Across
The chord joining the vertices is the major axis, and its midpoint is the ______ of the ellipse.
A collection of points satisfying a geometric property
A(n) _____ section (or simply _____) is the intersection of a plane and a double-napped cone.
If the vertex of a parabola is at the origin, then the equation takes one of the following forms. x² = 4py (________ axis)
A(n) ________ is the set of all points (x, y) in a plane that are equidistant from a fixed line, called the directrix, and a fixed point, called the focus, not on the line.
The sum of the distances from any point on the ellipse to the two foci is ________.
A hyperbola 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 ______ points, called foci, is constant.
The specific focal chord perpendicular to the axis of the parabola is called the latus ______.
The technique of __________ the square is used to write the equation in Example 2 in standard form.
The ____________ e of an ellipse is given by the ratio e = c/a.
In a parabolic reflector, light is reflect in ________ rays.
If the vertex of a parabola is at the origin, then the equation takes one of the following forms. y² = 4py (__________ axis)
An ellipse is the set of all points (x, y) in a plane, the sum of whose distances from two distinct fixed points, called ____, is constant.
In Section 2.1, you learned that the graph of the _________ function f(x) = ax² + bx + c is a parabola that opens upward or downward.
The line segment connecting the vertices is the __________ axis, and the midpoint of the ___________ axis is the center of the hyperbola.
If you let (x, y) be ___ point on the ellipse, then the sum of the distances between (x, y) and the two foci must also be 2a.
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.
The graph of a hyperbola has two disconnected parts called ________.
Down
A(n) _______ is the set of all points (x, y) in a plane, the sum of whose distances from two distinct fixed points, called foci, is constant.
To measure the ________ of an ellipse, you can use the concept of eccentricity.
A line segment that passes through the focus of a parabola and has endpoints on the parabola is called a focal _____.
The ________ form of the equation of a parabola with vertex at (h, k) is as follows. (x -h)² = 4p(y - k), p ≠ 0 and (y - k)² = 4p(x - h), p ≠ 0
A parabola is the set of all points (x, y) in a plane that are equidistant from a fixed line, called the directrix, and a fixed point, called the _____, not on the line.
The ___________ Property of a Parabola states that the tangent line to a parabola at a point P makes equal angles with the following two lines: 1. The line passing through P and the focus; 2. The axis of the parabola
Each hyperbola has two __________ that intersect at the center of the hyperbola.
The line segment of length 2b joining (h, k + b) and (h, k - b) is the _________ axis of the hyperbola.
Notice in Figure 10.7 that in the formation of the four basic conics, the intersecting plane does not pass through the vertex of the cone. When the plane does pass through the vertex, the resulting figure is a(n) __________ conic, as shown in Figure 10.8.
You can _______ a conic from its general equation Ax² + Cy² + Dx + Ey + F = 0 using the test on page 719.
The line segment connecting the vertices is the transverse axis, and the ________ of the transverse axis is the center of the hyperbola.
The chord joining the vertices is the ______ axis of the ellipse.
The chord perpendicular to the major axis at the center is the _____ axis of the ellipse.
The line through the two foci __________ the hyperbola at two points called the vertices.
A(n) _________ 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 foci, is constant.
The absolute value of the differences of the distances from any point on the hyperbola to the two foci is constant. Using a vertex, this constant value is = 2a or simply the _______ of the transverse axis.
The standard form of the ________ of an ellipse with center (h, k) and major and minor axes of lengths 2a and 2b, respectively, where 0 < b < a, is (x - h)²/a² + (y - k)²/b² = 1 (Major axis is horizontal) and (x - h)²/b² + (y - k)²/a² = 1 (Major axis is vertical)
The standard ____ of the equation of a hyperbola with center (h, k) is (x - h)²/a² - (y - k)²/b² = 1 (Transverse axis is horizontal) and (y - k)²/a² - (x - h)²/b² = 1 (Transverse axis is vertical)
A parabola is 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 focus, not on the line.
The asymptotes pass through the vertices of a _________ of dimensions 2a by 2b, with its center at (h, k).
The line through the foci intersects the ellipse at two points called ________.
The _______ of a parabola is the midpoint between the focus and the directrix.
The ____ [of symmetry] of the parabola is the line passing through the focus and the vertex.