This document discusses how to graph and write the equation of a hyperbola. It explains that a hyperbola has one set of intercepts on either the x-axis or y-axis depending on the signs of p and q in the standard form of the equation. It provides examples of writing equations in standard form and finding the center, asymptotes, and transverse axis to graph hyperbolas. The goal is to teach students how to recognize, write the equation of, and graph hyperbolas.

1. Aim: How do we graph, recognize, and write the equation of a hyperbola? MB43 3/19/09 Lomas Do Now: Find a, b, and the center of (x-3) 2 + 4(y+2) 2 = 36 What shape? How can you tell? HW Review: 3, 7 4x 2 + 9y 2 = 36 2x 2 + 2y 2 = 8 2x 2 - 2y 2 = 32 HW: Read 528-532 Do 532-3 #5,6,8

2. Aim: How do we graph, recognize, and write the equation of a hyperbola? 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 MB43 3/19/09 Lomas x 2 y 2 a2 b 2 + = 1 - x 2 y 2 a2 b 2 - = 1 HW: Read 528-532 Do 532-3 #5,6,8

4. Aim: How do we graph, recognize, and write the equation of a hyperbola? 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. MB43 3/19/09 Lomas HW: Read 528-532 Do 532-3 #5,6,8

5. Aim: How do we graph, recognize, and write the equation of a hyperbola? 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. W hat is the length of the transverse axis? MB43 3/19/09 Lomas HW: Read 528-532 Do 532-3 #5,6,8

6. Aim: How do we graph, recognize, and write the equation of a hyperbola? 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? MB43 3/19/09 Lomas HW: Read 528-532 Do 532-3 #5,6,8

7. Aim: How do we graph, recognize, and write the equation of a hyperbola? The asymptotes are two lines that will guide us in graphing hyperbolas Find the asymptotes of 25x 2 - 4y 2 = 100 and graph MB43 3/19/09 Lomas y = x b a -b a y = x HW: Read 528-532 Do 532-3 #5,6,8

8. Aim: How do we graph, recognize, and write the equation of a hyperbola? 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 MB43 3/19/09 Lomas HW: Read 528-532 Do 532-3 #5,6,8

9. Aim: How do we graph, recognize, and write the equation of a hyperbola? What is the center of this hyperbola? What are the equations of the asymptotes? Graph. (x-2) 2 (y+3) 2 9 25 - = 1 MB43 3/19/09 Lomas HW: Read 528-532 Do 532-3 #5,6,8