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Definition: A hyperbola is the set of points P(x,y) in a plane such that the absolute value of the difference between the distances from P to two fixed points in the plane, F 1 and F 2, called the foci, is a constant. 9.5 Hyperbolas

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Transverse axis Conjugate Axis Vertices Co-vertices Center Foci Asymptotes (2a) length of V to V (2b) length of CV to CV Endpoints of TA Endpoints of CA Intersection of the 2 axes Lie on inside of hyperbola Horizontal Vertical (When centered at the origin) 9.5 Hyperbolas

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Notes: a 2 is always the denominator of the ________ term when the equation is written in standard form. _________ axis can be longer or ____________ The length of the transverse axis is _________ he length of the conjugate axis is _________ a 2 + b 2 = c 2 9.5 Hyperbolas 1st Eithershorter 2a 2b

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Example 1: Write the standard equation of the hyperbola with vertices (-4,0) and (4,0) and co-vertices (0, -3) and (0, 3). Sketch the graph.

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Example 2: Write the standard equation of the hyperbola with V(-7, 0) (7, 0) and CV (0,-4) (0, 4).

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Example 3: Write the standard equation of the hyperbola with F (-1, 1) (5, 1) and V (0, 1) (4, 1).

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Example 4: Write the standard equation of the hyperbola with F (3, -3) (3, 7) and V (3, -1) (3, 5). Don’t forget! x and h are BFFs! So are y and k! Don’t split them up!

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Example 5: Find the equation of the asymptotes and the coordinates of the vertices for the graph of Then graph the hyperbola.

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Example 6: The equation x 2 – y 2 –6x –10y –20 = 0 represents a hyperbola. Write the standard equation of the hyperbola. Give the coordinates of the center, vertices, co-vertices, and foci. Then graph the hyperbola.

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Example 7: The equation –2x 2 + y 2 + 4x + 6y + 3 = 0 represents a hyperbola. Write the standard equation of the hyperbola. Give the coordinates of the center, vertices, co-vertices, and foci. Then graph the hyperbola.

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Example 8: The equation 4x 2 – 25y 2 – 8x + 100y – 196 = 0 represents a hyperbola. Write the standard equation of the hyperbola. Give the coordinates of the center, vertices, co-vertices, and foci. Then graph the hyperbola.

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