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Math1050 CH07

Analytic Geometry (ellipeses, parabolas, hyperbolas)

Side 1Side 2
When 2 different lines intersect and one is rotated around the other (the axis) it is called a ___. cone
Where the lines of conics intersect it is called the ___. vertex, V
The lines of conics that are swept out to create a cone are called ___. generators
Each of the 2 parts of a cone is called a ___. nappe
A plane trough a cone perpendicular to the axis is a ___. circle
A plane trough a cone at an angle to the axis that is less than the angle of the generators is called an ___. ellipse
A plane trough a cone that is the same angle as the generator is a ___. parabola
A plane trough a cone at an angle to the axis that is greater than the angle of the generators is called an ___. hyperbola
The graph of a quadratic function is a ___. parabola
A parabola is the collection of all points P in the plane that are ___ from a fixed point F as they are from a fixed line D. the same distance d
In a parabola, F is called the ___. focus
In a parabola, D is called the ___. directrix
In a parabola, the line perpendicular to the directrix trough which F passes is called the ___. axis of symmetry
In a parabola, the point directly between F and the directrix is called the ___. vertex
In a parabola, a is the distance from ___ to ___, and -a is the distance between ___ and ___. V, F, V, D
For a right opening parabola, if V is on the origin, then the equation for the directrix is ___. x=-a
What is the equation for a parabola? (y-k)^2 = 4a(x-h) or y-k = +- (4a(x-h))^1/2 or y = (x-h)^2 + k
In a parabola, the line that is parallel to D that connects F to the points above and below F on the graph is called the ___. latus rectum
In a parabola, the length of the latus rectum is ___. 4a
In a parabola, the length of the latus rectum from F to the graph is ___. 2a
In a parabola, the 2 points on the graph that the latus rectum pass through are ___ and ___. (For a right-opening parabola) (a, 2a), (a, -2a)
The shape formed by rotating a parabola around its line of symmetry is called a ___. paraboloid of revolution
In a paraboloid of revolution, if a light is placed at F, light will reflect ___ to the axis of symmetry. (and vice versa if it is going the other direction) parallel
The collection of points in a plane, the sum of whose distances from 2 fixed points called foci, is constant is called an ___. ellipse
For an ellipse, F are the ___. foci
For an ellipse, the line containing the foci is the ___. major axis
For an ellipse, the line perpendicular to the major axis is called the ___. minor axis
For an ellipse, the 2 points where the graph passes through the major axis are called ___. vertices, V
For an ellipse, the lengths between the two F and a point on the graph are labeled ___. d
For a horizontal ellipse centered at the origin, V is at the points ___ and ___. (-a, 0), (a, 0)
For a horizontal ellipse centered at the origin, F is at the points ___ and ___. (-c, 0), (c, 0)
For a horizontal ellipse centered at the origin, the graph intersects the y-axis at the points ___ and ___. (0, b), (0, -b)
What is the equation for an ellipse with a horizontal major axis? (x-h)^2/a^2 + (y-k)^2/b^2 = 1
What is the equation for an ellipse with a vertical major axis? (x-h)^2/b^2 + (y-k)^2/a^2 = 1
A ___ is all points in a plane, the difference of whose distances from two fixed points, called foci, is constant. hyperbola
For a hyperbola, the line containing the foci is the ___. transverse axis
For a hyperbola, the point directly between the two F or the two V is the ___. center
For a hyperbola, the line perpendicular to the transverse axis is the ___. conjugate axis
For a hyperbola, each line of the graph is called a ___. branch
For a hyperbola, the points where the graph crosses the transverse axis are the ___. vertices, V
For a hyperbola, a is the distance from the ___ to the ___. center, vertex
For a hyperbola, c is the distance from the ___ to the ___. center, focus
For a hyperbola, d is the distance from the ___ to ___. focus, a point on the graph
For a hyperbola, the difference of the distances from P to the F equals ___. +- 2a
For a hyperbola, d_1 - d_2 = ___ 2a
What is the equation for a hyperbola with a horizontal transverse axis? (x-h)^2/a^2 - (y-k)^2/b^2 = 1
What is the equation for a hyperbola with a vertical transverse axis? (y-k)^2/a^2 - (x-h)^2/b^2 = 1
For a hyperbola, to draw the asymptotes, draw a box with sides ___ and ___ centered at (h,k) and draw diagonal lines through the corners. 2a, 2b
For an ellipse, b^2 = ___. a^2 - c^2 (a^2 - b^2 = c^2)
For a hyperbola, b^2 = ___. c^2 - a^2 (a^2 + b^2 = c^2)
For a hyperbola with a horizontal transverse axis, what are the asymptotes? y = (b/a)x and y = -(b/a)x
For a hyperbola with a vertical transverse axis, what are the asymptotes? y = (a/b)x and y = -(a/b)x
Created by: drjolley