Warm Up: What is it? Ellipse or circle?

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Presentation transcript:

Warm Up: What is it? Ellipse or circle?

9.5 Hyperbolas 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.

9.5 Hyperbolas 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 Notes: a2 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 _________ The length of the conjugate axis is _________ a2 + b2 = c2 1st Either shorter 2a 2b

a2 always comes 1st!

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.

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

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 BFFs! 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 coordinates of the vertices, co-vertices, and foci for the graph of Then graph the hyperbola.

Tonight’s HW: p.192 #2-14 evens

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.

Quiz p.970 – Lesson 9.4 # 1,10,11 p. 971 – Lesson 9.5 # 1, 2, 6, 8 Homework Worksheet 9.4 #2,3,5,6,10 AND 9.5 #4

What is the equation?

What is the equation?

What is the equation?

What is the equation?

What is the equation?

What is the equation?

What is the equation?

What is the equation?

Place the equation with the graph.