5.4 Hyperbolas (part 2) 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.

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Presentation transcript:

5.4 Hyperbolas (part 2) 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, F1 and F2, called the foci, is a constant. Doted lines are not part of the graph

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

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

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

Example 6: The equation x2 – y2 – 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.

Example 7: The equation –2x2 + y2 + 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.

Example 8: The equation 4x2 – 25y2 – 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.

Homework Pg. 193, 1 – 13 all