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HYPERBOLAS

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…. HYPERBOLAS.

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HYPERBOLAS

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  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 = √1 + 16 = √17

  17. HYPERBOLAS EXAMPLE # 2 :Find the center, major axis vertices, foci, and asymptote equation for A = 4 B = 1 C = √1 + 16 = √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 = √1 + 16 = √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 = √1 + 16 = √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 = √1 + 16 = √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 = √1 + 16 = √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 = √1 + 16 = √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 = √1 + 16 = √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 = √1 + 16 = √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 = √1 + 16 = √17 Center ( - 4 , 2 ) Major Axis Vertices ( - 4 , 3 ) , ( - 4 , 1 ) Foci ( -4 , 2 ± √17 ) Asymptote equation : Next, sketch your hyperbola…

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