Hyperbolas and Circles
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Transcript of Hyperbolas and Circles
![Page 1: Hyperbolas and Circles](https://reader030.fdocuments.in/reader030/viewer/2022033022/5681332a550346895d9a1c7f/html5/thumbnails/1.jpg)
Hyperbolas and Circles
![Page 2: Hyperbolas and Circles](https://reader030.fdocuments.in/reader030/viewer/2022033022/5681332a550346895d9a1c7f/html5/thumbnails/2.jpg)
Learning Targets
To recognize and describe the characteristics of a hyperbola and circle.
To relate the transformations, reflections and translations of a hyperbola and circle to an equation or graph
![Page 3: Hyperbolas and Circles](https://reader030.fdocuments.in/reader030/viewer/2022033022/5681332a550346895d9a1c7f/html5/thumbnails/3.jpg)
Hyperbola
A hyperbola is also known as a rational function and is expressed as INSERT EQUATION
GRAPH
![Page 4: Hyperbolas and Circles](https://reader030.fdocuments.in/reader030/viewer/2022033022/5681332a550346895d9a1c7f/html5/thumbnails/4.jpg)
Hyperbola Characteristics
Graph
The characteristics of a hyperbola are:• Has no vertical or
horizontal symmetry• There are both horizontal
and vertical asymptotes• The domain and range is
limited
![Page 5: Hyperbolas and Circles](https://reader030.fdocuments.in/reader030/viewer/2022033022/5681332a550346895d9a1c7f/html5/thumbnails/5.jpg)
Locator Point
Graph
The locator point for this function is where the horizontal and vertical asymptotes intersect.
Therefore we use the origin, (0,0).
![Page 6: Hyperbolas and Circles](https://reader030.fdocuments.in/reader030/viewer/2022033022/5681332a550346895d9a1c7f/html5/thumbnails/6.jpg)
Standard Form
![Page 7: Hyperbolas and Circles](https://reader030.fdocuments.in/reader030/viewer/2022033022/5681332a550346895d9a1c7f/html5/thumbnails/7.jpg)
Impacts of h and k
Graph
Based on the graph at the right what inputs/outputs can our function never have?
This point is known as the hyperbolas ‘hole’
![Page 8: Hyperbolas and Circles](https://reader030.fdocuments.in/reader030/viewer/2022033022/5681332a550346895d9a1c7f/html5/thumbnails/8.jpg)
Impacts of h and k
Graph
The coordinates of this hole are actually the values we cannot have in our domain and range.
Domain: all real numbers for x other than h
Range: all real numbers for y other than k
![Page 9: Hyperbolas and Circles](https://reader030.fdocuments.in/reader030/viewer/2022033022/5681332a550346895d9a1c7f/html5/thumbnails/9.jpg)
Impacts of h and k
Graph
This also means that our asymptotes can be identified as:
Vertical Asymptote: x=h
Horizontal Asymptote: y=k
![Page 10: Hyperbolas and Circles](https://reader030.fdocuments.in/reader030/viewer/2022033022/5681332a550346895d9a1c7f/html5/thumbnails/10.jpg)
Example #1
![Page 11: Hyperbolas and Circles](https://reader030.fdocuments.in/reader030/viewer/2022033022/5681332a550346895d9a1c7f/html5/thumbnails/11.jpg)
Example #2
![Page 12: Hyperbolas and Circles](https://reader030.fdocuments.in/reader030/viewer/2022033022/5681332a550346895d9a1c7f/html5/thumbnails/12.jpg)
Impacts of a
Graph
Our stretch/compression factor will once again change the shape of our function.
The multiple of the factor will will determine how close our graph is to the ‘hole’
The larger the a value, the further away our graph will be.
The smaller the a value , the closer our graph will be.
![Page 13: Hyperbolas and Circles](https://reader030.fdocuments.in/reader030/viewer/2022033022/5681332a550346895d9a1c7f/html5/thumbnails/13.jpg)
Example #3
Graph
![Page 14: Hyperbolas and Circles](https://reader030.fdocuments.in/reader030/viewer/2022033022/5681332a550346895d9a1c7f/html5/thumbnails/14.jpg)
Circle