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9.5 Hyperbolas PART 1 Hyperbola/Parabola Quiz: Friday Conics Test: March 26

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Definition of Hyperbola: A hyperbola is the set of points P(x,y) in a plane such that the absolute value of the difference between the distances P to two fixed points in the plane, f 1 and f 2, called the foci, is constant. P Q F1 F2

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What you need to know: A hyperbola has two axes of symmetry. One axis contains the TRANSVERSE axis of the hyperbola, (a,0) to (-a,0), and the other axis contains the CONJUGATE axis, from (0,-b) to (0,b). The endpoints of the TRANSVERSE are called vertices. The endpoints of the CONJUGATE are called co-vertices. The point in the VERY middle, is the center.

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Standard Equation of a Hyperbola CENTERED AT THE ORIGIN (0,0) Horizontal Vertical In both cases: a²+b²=c². (it switched from the ellipse!!!!) Length of the transverse is 2a and length of the conjugate is 2b AND NOTE: Transverse is NOT ALWAYS longer than the CONJUGATE!!!

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Example: Write the standard equation for the hyperbola with vertices at (0,-4) and (0,4) and co- vertices at (-3,0) and (3,0). Then Sketch the graph. Since the vertices lie along the y-axis, the equation is vertical. We know that a=4 and b=3.

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Example 1 Graph:

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You try: Write the standard equation for the hyperbola whose vertices are at V 1 (-5,0), and V 2 (5,0) and whose co-vertices are at C 1 (0,-6) and C 2 (0,6). Graph it!

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You Try Graph:

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Asymptotes: Given a hyperbola centered at the origin, you can find the asymptotes: Standard equation:

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Example 2: Find the equations for the asymptotes and coordinates of the vertices for the following equation. Then sketch the graph.

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Example 2 Graph:

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You Try: Find the equations of the asymptotes and the coordinates of the vertices for the graph below. Then sketch the graph.

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You Try Graph:

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Homework: Hyperbola WS #1 YOU HAVE TO PRACTICE!!!

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