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# Math1050 CH07

### Analytic Geometry (ellipeses, parabolas, hyperbolas)

Side 1 | Side 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 |