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Hyperbolas T

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This document discusses how to graph, recognize, and write the equation of a hyperbola. It explains that a hyperbola is formed when the coefficients of x2 and y2 have different signs. It also notes that hyperbolas only intersect one set of axes and that the signs of the coefficients determine which axis the intercepts lie on. The document provides examples of writing equations of hyperbolas in standard form and finding the asymptotes and transverse axis to graph hyperbolas.

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Aim: How do we graph, recognize, and write the equation of a hyperbola? MB43 10/22/08 Lomas Do Now: Circle or Ellipse? How can you tell? HW Review: 6, 8 4x 2 + 9y 2 = 36 2x 2 + 2y 2 = 8 2x 2 - 2y 2 = 32 HW: Read 528-532 Do 532-3 #3-6,8
Aim: How do we graph, recognize, and write the equation of a hyperbola? MB43 10/22/08 Lomas px 2 + qy 2 = s Is a hyperbola when p and q have different signs Just like ellipses, we want to get hyperbolas in the form: OR And it's done the same way HW: Read 528-532 Do 532-3 #3-6,8 x 2 y 2 a 2 b 2 + = 1 - x 2 y 2 a 2 b 2 - = 1
Aim: How do we graph, recognize, and write the equation of a hyperbola? MB43 10/22/08 Lomas Hyperbola's only have one set of intersects, because they only touch one set of axes We can tell which axis the intercepts are on by looking at the signs of p and q (or a 2 and b 2 ). Whichever one has the same sign as s will have the intercepts. HW: Read 528-532 Do 532-3 #3-6,8
Aim: How do we graph, recognize, and write the equation of a hyperbola? MB43 10/22/08 Lomas 25x 2 - 4y 2 = 100 Put into standard form What axis do the intercepts lie on? What are the intercepts? The transverse axis is the line segement that has the intercepts as its endpoints. What is the length of the transverse axis? HW: Read 528-532 Do 532-3 #3-6,8
Aim: How do we graph, recognize, and write the equation of a hyperbola? MB43 10/22/08 Lomas To graph 25x 2 - 4y 2 = 100 we still don't have enough info, but what do we know so far? What do we still need to know? HW: Read 528-532 Do 532-3 #3-6,8
Aim: How do we graph, recognize, and write the equation of a hyperbola? MB43 10/22/08 Lomas The asymptotes are two lines that will guide us in graphing hyperbolas Find the asymptotes of 25x 2 - 4y 2 = 100 and graph HW: Read 528-532 Do 532-3 #3-6,8 y = x b a -b a y = x
Aim: How do we graph, recognize, and write the equation of a hyperbola? MB43 10/22/08 Lomas What axis is the tranverse axis a segment of? What is the length of the transverse axis? What are the equations of the asymptotes? Graph. 3x 2 - 12y 2 = -24 HW: Read 528-532 Do 532-3 #3-6,8
Aim: How do we graph, recognize, and write the equation of a hyperbola? MB43 10/22/08 Lomas What is the center of this hyperbola? What are the equations of the asymptotes? Graph. (x-2) 2 (y+3) 2 9 25 - = 1 HW: Read 528-532 Do 532-3 #3-6,8

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Hyperbolas T

  • 1. Aim: How do we graph, recognize, and write the equation of a hyperbola? MB43 10/22/08 Lomas Do Now: Circle or Ellipse? How can you tell? HW Review: 6, 8 4x 2 + 9y 2 = 36 2x 2 + 2y 2 = 8 2x 2 - 2y 2 = 32 HW: Read 528-532 Do 532-3 #3-6,8
  • 2. Aim: How do we graph, recognize, and write the equation of a hyperbola? MB43 10/22/08 Lomas px 2 + qy 2 = s Is a hyperbola when p and q have different signs Just like ellipses, we want to get hyperbolas in the form: OR And it's done the same way HW: Read 528-532 Do 532-3 #3-6,8 x 2 y 2 a 2 b 2 + = 1 - x 2 y 2 a 2 b 2 - = 1
  • 3. Aim: How do we graph, recognize, and write the equation of a hyperbola? MB43 10/22/08 Lomas Hyperbola's only have one set of intersects, because they only touch one set of axes We can tell which axis the intercepts are on by looking at the signs of p and q (or a 2 and b 2 ). Whichever one has the same sign as s will have the intercepts. HW: Read 528-532 Do 532-3 #3-6,8
  • 4. Aim: How do we graph, recognize, and write the equation of a hyperbola? MB43 10/22/08 Lomas 25x 2 - 4y 2 = 100 Put into standard form What axis do the intercepts lie on? What are the intercepts? The transverse axis is the line segement that has the intercepts as its endpoints. What is the length of the transverse axis? HW: Read 528-532 Do 532-3 #3-6,8
  • 5. Aim: How do we graph, recognize, and write the equation of a hyperbola? MB43 10/22/08 Lomas To graph 25x 2 - 4y 2 = 100 we still don't have enough info, but what do we know so far? What do we still need to know? HW: Read 528-532 Do 532-3 #3-6,8
  • 6. Aim: How do we graph, recognize, and write the equation of a hyperbola? MB43 10/22/08 Lomas The asymptotes are two lines that will guide us in graphing hyperbolas Find the asymptotes of 25x 2 - 4y 2 = 100 and graph HW: Read 528-532 Do 532-3 #3-6,8 y = x b a -b a y = x
  • 7. Aim: How do we graph, recognize, and write the equation of a hyperbola? MB43 10/22/08 Lomas What axis is the tranverse axis a segment of? What is the length of the transverse axis? What are the equations of the asymptotes? Graph. 3x 2 - 12y 2 = -24 HW: Read 528-532 Do 532-3 #3-6,8
  • 8. Aim: How do we graph, recognize, and write the equation of a hyperbola? MB43 10/22/08 Lomas What is the center of this hyperbola? What are the equations of the asymptotes? Graph. (x-2) 2 (y+3) 2 9 25 - = 1 HW: Read 528-532 Do 532-3 #3-6,8