Presentation on theme: "What is it?. 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."— Presentation transcript:
What is it?
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
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: 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
a 2 always comes 1 st !
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.
Example 2: Write the standard equation of the hyperbola with V (0,-4) (0, 4) and CV(-7, 0) (7, 0) a= b= c= V: CV: Foci: Center:
Example 5: Find the equation of the asymptotes and the coordinates of the vertices for the graph of Then graph the hyperbola. a= b= c= V: CV: Foci: Center: