Pre-Cal 40S Slides December 17, 2007
-
Upload
darren-kuropatwa -
Category
Technology
-
view
2.037 -
download
4
description
Transcript of Pre-Cal 40S Slides December 17, 2007
![Page 1: Pre-Cal 40S Slides December 17, 2007](https://reader034.fdocuments.in/reader034/viewer/2022052310/5559cacfd8b42a93208b47bc/html5/thumbnails/1.jpg)
12.3 Hyperbolas
The Anatomy of the Hyperbola
![Page 2: Pre-Cal 40S Slides December 17, 2007](https://reader034.fdocuments.in/reader034/viewer/2022052310/5559cacfd8b42a93208b47bc/html5/thumbnails/2.jpg)
The Standard Form for the Equation of a Hyperbola
Horizontal Orientation Vertical Orientation
Similarities Differences
• all variables are squared • they both equal 1• denominators tell you the semi-conjugate and semi-transverse axes• both equations are differences• "h" is always with "x", and "k" is always with "y"• they both tell you the centre (h,k)
• the positive term in a horizontal hyperbola is the x term for a vertical hyperbola y is positive• the denominator has switched• a is underneath y in a vertical hyperbola, a is underneath x in the horizontal hyperbola
![Page 3: Pre-Cal 40S Slides December 17, 2007](https://reader034.fdocuments.in/reader034/viewer/2022052310/5559cacfd8b42a93208b47bc/html5/thumbnails/3.jpg)
Conics Animations Source
![Page 4: Pre-Cal 40S Slides December 17, 2007](https://reader034.fdocuments.in/reader034/viewer/2022052310/5559cacfd8b42a93208b47bc/html5/thumbnails/4.jpg)
Conics Animations Source
![Page 5: Pre-Cal 40S Slides December 17, 2007](https://reader034.fdocuments.in/reader034/viewer/2022052310/5559cacfd8b42a93208b47bc/html5/thumbnails/5.jpg)
Conics Animations Source
![Page 6: Pre-Cal 40S Slides December 17, 2007](https://reader034.fdocuments.in/reader034/viewer/2022052310/5559cacfd8b42a93208b47bc/html5/thumbnails/6.jpg)
Conics Animations Source
![Page 7: Pre-Cal 40S Slides December 17, 2007](https://reader034.fdocuments.in/reader034/viewer/2022052310/5559cacfd8b42a93208b47bc/html5/thumbnails/7.jpg)
For the hyperbola whose equation is given below.
(i) Write the equation in standard form(ii) Determine the lengths of the transverse and conjugate axes, the
coordinates of the verticies and foci, and the equations of the asymptotes.(iii) Sketch a graph of the hyperbola.
![Page 8: Pre-Cal 40S Slides December 17, 2007](https://reader034.fdocuments.in/reader034/viewer/2022052310/5559cacfd8b42a93208b47bc/html5/thumbnails/8.jpg)
![Page 9: Pre-Cal 40S Slides December 17, 2007](https://reader034.fdocuments.in/reader034/viewer/2022052310/5559cacfd8b42a93208b47bc/html5/thumbnails/9.jpg)
![Page 10: Pre-Cal 40S Slides December 17, 2007](https://reader034.fdocuments.in/reader034/viewer/2022052310/5559cacfd8b42a93208b47bc/html5/thumbnails/10.jpg)
For the hyperbola whose equation is given below.
(i) Write the equation in standard form(ii) Determine the lengths of the transverse and conjugate axes, the
coordinates of the verticies and foci, and the equations of the asymptotes.(iii) Sketch a graph of the hyperbola. SLOPE INTERCEPT FORM
![Page 11: Pre-Cal 40S Slides December 17, 2007](https://reader034.fdocuments.in/reader034/viewer/2022052310/5559cacfd8b42a93208b47bc/html5/thumbnails/11.jpg)
For each ellipse whose equation is given below
(i) Write the equation in standard form(ii) Determine the lengths of the major and minor axes, the coordinates
of the verticies, and the coordinates of the foci.(iii) Sketch a graph of the ellipse.
![Page 12: Pre-Cal 40S Slides December 17, 2007](https://reader034.fdocuments.in/reader034/viewer/2022052310/5559cacfd8b42a93208b47bc/html5/thumbnails/12.jpg)
The foci of an ellipse are F1(2, 3) and F2(-2, 3), and the sum of the focal radii is 6 units. Use the definition of an ellipse to derive the equation of this ellipse.
![Page 13: Pre-Cal 40S Slides December 17, 2007](https://reader034.fdocuments.in/reader034/viewer/2022052310/5559cacfd8b42a93208b47bc/html5/thumbnails/13.jpg)
Find the radius, and the coordinates of the centre of the circle:
![Page 14: Pre-Cal 40S Slides December 17, 2007](https://reader034.fdocuments.in/reader034/viewer/2022052310/5559cacfd8b42a93208b47bc/html5/thumbnails/14.jpg)
The foci of a hyperbola are F1(6, 0) and F2(-6, 0), and the difference of the focal radii is 4 units. Use the definition of a hyperbola to derive the equation of this hyperbola.
![Page 15: Pre-Cal 40S Slides December 17, 2007](https://reader034.fdocuments.in/reader034/viewer/2022052310/5559cacfd8b42a93208b47bc/html5/thumbnails/15.jpg)
Determine the equaiton of a parabola defined by the given conditions.
The vertex is V(-1, 3) and the equation of the directrix is x - 2 = 0
![Page 16: Pre-Cal 40S Slides December 17, 2007](https://reader034.fdocuments.in/reader034/viewer/2022052310/5559cacfd8b42a93208b47bc/html5/thumbnails/16.jpg)
A rock is kicked off a vertical cliff and falls in a parabolic path to the water below. The cliff is 40 m high and the rock hits the water 10 m from the base of the cliff. What is the horizontal distance of the rock from the cliff face when the rock is at a height of 30 m above the water?
![Page 17: Pre-Cal 40S Slides December 17, 2007](https://reader034.fdocuments.in/reader034/viewer/2022052310/5559cacfd8b42a93208b47bc/html5/thumbnails/17.jpg)
A hyperbola has centre (0, 0) and one vertex A .
(c) Find the value of b if L(3, b) is on the hyperbola.
(b) Find the value of a if K(a, 2) is on the hyperbola.
(a) Find the equation of the hyperbola if it passes through J(9, 5)
![Page 18: Pre-Cal 40S Slides December 17, 2007](https://reader034.fdocuments.in/reader034/viewer/2022052310/5559cacfd8b42a93208b47bc/html5/thumbnails/18.jpg)
Consider the parabola y2 - 20x + 2y + 1 = 0. Write the equation in standard form, find the coordinates of the vertex and focus and the equation of the directrix.
![Page 19: Pre-Cal 40S Slides December 17, 2007](https://reader034.fdocuments.in/reader034/viewer/2022052310/5559cacfd8b42a93208b47bc/html5/thumbnails/19.jpg)
Write the equation of the circle x2 + y2 + 2x - 10y + 25 = 0 in standard form and find the centre and the radius.
![Page 20: Pre-Cal 40S Slides December 17, 2007](https://reader034.fdocuments.in/reader034/viewer/2022052310/5559cacfd8b42a93208b47bc/html5/thumbnails/20.jpg)
The parabola y2 - x + 4y + k = 0 passes through the point (12, 1). Find the coordinates of the vertex and sketch the graph.
![Page 21: Pre-Cal 40S Slides December 17, 2007](https://reader034.fdocuments.in/reader034/viewer/2022052310/5559cacfd8b42a93208b47bc/html5/thumbnails/21.jpg)
A point P(x, y) moves such that it is always equidistant from the point A(2, 3) and the line y = -1. Determine the equation of this locus in standard form.
![Page 22: Pre-Cal 40S Slides December 17, 2007](https://reader034.fdocuments.in/reader034/viewer/2022052310/5559cacfd8b42a93208b47bc/html5/thumbnails/22.jpg)
An ellipse has centre (-2, 4) and one vertex A(8, 4).
(a) Find the equation of the ellipse if it passes through R(4, 8).(b) Find the value of c if S(c, 7) is on the ellipse.(c) Find the value of d if T(3, d) is on the ellipse.