Presentation on theme: "9.5 Hyperbolas PART 1 Hyperbola/Parabola Quiz: Friday Conics Test: March 26."— Presentation transcript:
9.5 Hyperbolas PART 1 Hyperbola/Parabola Quiz: Friday Conics Test: March 26
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
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.
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!!!
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.