Download presentation

Presentation is loading. Please wait.

Published byRachel Pigeon Modified over 2 years ago

1
HYPERBOLAS The equation of a hyperbola is almost exactly that of an ellipse. The only change that occurs is there is a minus sign between the terms. ALSO, be careful, the x and y terms can become switched, so be aware that y could lead. Lastly, to find c…

2
HYPERBOLAS The equation of a hyperbola is almost exactly that of an ellipse. The only change that occurs is there is a minus sign between the terms. ALSO, be careful, the x and y terms can become switched, so be aware that y could lead. Hyperbolas with center ( 0 , 0 ). Notice the positive part always leads.

3
HYPERBOLAS The equation of a hyperbola is almost exactly that of an ellipse. The only change that occurs is there is a minus sign between the terms. ALSO, be careful, the x and y terms can become switched, so be aware that y could lead. Graph opens left / right

4
HYPERBOLAS The equation of a hyperbola is almost exactly that of an ellipse. The only change that occurs is there is a minus sign between the terms. ALSO, be careful, the x and y terms can become switched, so be aware that y could lead. Graph opens up / down

5
HYPERBOLAS The equation of a hyperbola is almost exactly that of an ellipse. The only change that occurs is there is a minus sign between the terms. ALSO, be careful, the x and y terms can become switched, so be aware that y could lead. Standard form for each type…

6
HYPERBOLAS The equation of a hyperbola is almost exactly that of an ellipse. The only change that occurs is there is a minus sign between the terms. ALSO, be careful, the x and y terms can become switched, so be aware that y could lead. What we will find for each… a , b , and c Center : ( h , k ) Major Axis Vertices : ( x1 , y1 ) , ( x2 , y2 ) Foci : ( x , y ) Asymptote Equation : These are dashed lines that the graph does not cross…

7
HYPERBOLAS Lets jump right in… EXAMPLE : Find the center, major axis vertices, foci, and asymptote equation for

8
HYPERBOLAS Lets jump right in… EXAMPLE : Find the center, major axis vertices, foci, and asymptote equation for Center ( x , y ) Major vertices ( x1 , y1 ) , ( x2 , y2 ) Foci ( x , y ) Asymptote Eq.

9
HYPERBOLAS Lets jump right in… EXAMPLE : Find the center, major axis vertices, foci, and asymptote equation for a = 3 b = 2 c = √13 Center ( x , y ) Major vertices ( x1 , y1 ) , ( x2 , y2 ) Foci ( x , y ) Asymptote Eq.

10
HYPERBOLAS Lets jump right in… EXAMPLE : Find the center, major axis vertices, foci, and asymptote equation for a = 3 b = 2 c = √13 Center ( 0 , 0 ) Major vertices ( x1 , y1 ) , ( x2 , y2 ) Foci ( x , y ) Asymptote Eq.

11
HYPERBOLAS Lets jump right in… EXAMPLE : Find the center, major axis vertices, foci, and asymptote equation for a = 3 b = 2 c = √13 ±3 Center ( 0 , 0 ) ( x ) Major vertices ( 3 , 0 ) , ( - 3 , 0 ) Foci ( x , y ) Asymptote Eq. x leads so x is Major axis… adjust h by ± a

12
HYPERBOLAS Lets jump right in… EXAMPLE : Find the center, major axis vertices, foci, and asymptote equation for a = 3 b = 2 c = √13 ±3 Center ( 0 , 0 ) ( x ) Major vertices ( 3 , 0 ) , ( - 3 , 0 ) Foci ( x , y ) Asymptote Eq. Foci is on major ( x )… Adjust x by ± c

13
HYPERBOLAS Lets jump right in… EXAMPLE : Find the center, major axis vertices, foci, and asymptote equation for a = 3 b = 2 c = √13 ±3 Center ( 0 , 0 ) ( x ) Major vertices ( 3 , 0 ) , ( - 3 , 0 ) Foci ( 0 ± √13 , 0 ) Asymptote Eq. Foci is on major ( x )… Adjust x by ± c

14
HYPERBOLAS Lets jump right in… EXAMPLE : Find the center, major axis vertices, foci, and asymptote equation for a = 3 b = 2 c = √13 ±3 Center ( 0 , 0 ) ( x ) Major vertices ( 3 , 0 ) , ( - 3 , 0 ) Foci ( 0 ± √13 , 0 ) Asymptote Eq.

15
HYPERBOLAS EXAMPLE # 2 : Find the center, major axis vertices, foci, and asymptote equation for

16
HYPERBOLAS EXAMPLE # 2 : Find the center, major axis vertices, foci, and asymptote equation for A = 4 B = 1 C = √ = √17

17
HYPERBOLAS EXAMPLE # 2 : Find the center, major axis vertices, foci, and asymptote equation for A = 4 B = 1 C = √ = √17 Center ( - 4 , 2 ) Notice that y leads, so be careful in your order

18
HYPERBOLAS EXAMPLE # 2 : Find the center, major axis vertices, foci, and asymptote equation for A = 4 B = 1 C = √ = √17 ±1 Center ( - 4 , 2 ) Major Axis Vertices ( - 4 , 3 ) , ( - 4 , 1 ) - y is positive so the major axis is y change y by ± b

19
HYPERBOLAS EXAMPLE # 2 : Find the center, major axis vertices, foci, and asymptote equation for A = 4 B = 1 C = √ = √17 ±√17 Center ( - 4 , 2 ) Major Axis Vertices ( - 4 , 3 ) , ( - 4 , 1 ) Foci ( -4 , 2 ± √17 ) Foci lies on major axis change y by ± c

20
HYPERBOLAS EXAMPLE # 2 : Find the center, major axis vertices, foci, and asymptote equation for A = 4 B = 1 C = √ = √17 Center ( - 4 , 2 ) Major Axis Vertices ( - 4 , 3 ) , ( - 4 , 1 ) Foci ( -4 , 2 ± √17 ) Asymptote equation :

21
HYPERBOLAS EXAMPLE # 2 : Find the center, major axis vertices, foci, and asymptote equation for A = 4 B = 1 C = √ = √17 Center ( - 4 , 2 ) Major Axis Vertices ( - 4 , 3 ) , ( - 4 , 1 ) Foci ( -4 , 2 ± √17 ) Asymptote equation : To graph, 1st plot center…

22
HYPERBOLAS EXAMPLE # 2 : Find the center, major axis vertices, foci, and asymptote equation for A = 4 B = 1 C = √ = √17 Center ( - 4 , 2 ) Major Axis Vertices ( - 4 , 3 ) , ( - 4 , 1 ) Foci ( -4 , 2 ± √17 ) Asymptote equation : Next, plot the major vertices…

23
HYPERBOLAS EXAMPLE # 2 : Find the center, major axis vertices, foci, and asymptote equation for A = 4 B = 1 C = √ = √17 Center ( - 4 , 2 ) Major Axis Vertices ( - 4 , 3 ) , ( - 4 , 1 ) Foci ( -4 , 2 ± √17 ) Asymptote equation : Next, create a rectangle based on your slope in the asymptote equation…

24
HYPERBOLAS EXAMPLE # 2 : Find the center, major axis vertices, foci, and asymptote equation for A = 4 B = 1 C = √ = √17 Center ( - 4 , 2 ) Major Axis Vertices ( - 4 , 3 ) , ( - 4 , 1 ) Foci ( -4 , 2 ± √17 ) Asymptote equation : Next, sketch your asymptote lines

25
HYPERBOLAS EXAMPLE # 2 : Find the center, major axis vertices, foci, and asymptote equation for A = 4 B = 1 C = √ = √17 Center ( - 4 , 2 ) Major Axis Vertices ( - 4 , 3 ) , ( - 4 , 1 ) Foci ( -4 , 2 ± √17 ) Asymptote equation : Next, sketch your hyperbola…

Similar presentations

OK

10.4 Hyperbolas JMerrill 2010. Definition A hyperbola is the set of all points in a plane, the difference of whose distances from two distinct fixed point.

10.4 Hyperbolas JMerrill 2010. Definition A hyperbola is the set of all points in a plane, the difference of whose distances from two distinct fixed point.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on job evaluation and job rotation Ppt on radio station Ppt on book review writing Ppt on water scarcity pictures Ppt on life cycle of a frog Ppt on channels of distribution for a product Ppt on network theory tutorials Ppt on depth first search youtube Ppt on micro controller traffic light Addition for kids ppt on batteries