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# Hyperbolas

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### Hyperbolas

1. 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. 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
3. 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
4. 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
5. 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
6. 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
7. 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
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