Conics 10 5 Hyperbola Important Vocabulary and steps

Conics 10. 5 Hyperbola • • • Important Vocabulary (and steps) Transverse Axis Vertices Central Rectangle Asymptotes Graph Foci

y x a 2 = 36 and b 2 = 4 Because x is first, the transverse axis is horizontal and the vertices are (± 6, 0). Use the a and b values to draw the central rectangle. The asymptotes are Remember that the y number is ALWAYS on top for the asymptotes equation. Sketch the hyperbola’s branches through the vertices and approaching the asymptotes.

y You find the Foci by using Pythagorean Theorem. c 2 = a 2 + b 2 c 2 = 36 + 4 c 2 = 40 x

y Find the foci of each hyperbola and graph it. Transverse axis is horizontal or vertical? Vertical because y is first What are the vertices on the y axis? ( 0, 5) and (0, -5) x What is the central rectangle’s dimensions? The horizontal goes with x So from -8 to 8 is 16 The vertical goes with y So from -5 to 5 is 10 What are the equations of the Remember that the y number asymptotes? is ALWAYS on top for the asymptotes equation.

y You find the Foci by using Pythagorean Theorem. c 2 = a 2 + b 2 c 2 = 25 + 64 c 2 = 89 x

4 y 2 – 16 x 2 = 64 How do you handle this? y x Horizontal or vertical transverse axis? y is first. Vertical Vertices? (0, ± 4) Central rectangle? 4 by 8 Asymptotes? Foci? c 2= 42 +22 c 2= 20 c=4. 5 Remember that the y number is ALWAYS on top for the asymptotes equation.

y Find the foci of each hyperbola and graph it. Transverse axis is horizontal or vertical? Horizontal because x is first What are the vertices on the x axis? ( 8, 0) and (-8, 0) What are the central rectangle’s dimensions? The horizontal goes with x So from -8 to 8 is 16 The vertical goes with y So from -4 to 4 is 8 What are the equations of the asymptotes? Foci? c 2= 82 +42 c 2= 64 + 16 c 2= 80 c = 8. 9 x

. Foci: Vertices: • The transverse axis is horizontal because the Foci are x numbers. • You have the a value (4) and the c value(5). Use those to find b. • c 2 = a 2 + b 2 • 5 2 = 4 2 + b 2 • 25 = 16 + b 2 • 9 = b 2 • 3=b What is the equation? y x