What is a hyperbola? Do Now: Define the literary term hyperbole.

What are the conic sections?  Circle, e=0  Parabola e=1  Ellipse, 0<e<1  Hyperbola, e>1  Circle, e=0  Parabola e=1  Ellipse, 0<e<1  Hyperbola, e>1

What is the technical definition of a hyperbola?  The locus of points such that the absolute value of the difference of the distances of any points on the locus from two fixed points is a constant.  Each of the fixed points is a focus of the hyperbola  The locus of points such that the absolute value of the difference of the distances of any points on the locus from two fixed points is a constant.  Each of the fixed points is a focus of the hyperbola

What is the equation of a hyperbola?  (x-h) 2 /a 2 –(y–k) 2 /b 2 =1 or (y–k) 2 /a 2 –(x– h) 2 /b 2 =1  (h, k) is the center of the hyperbola  2a is the length of the transverse axis.  The transverse axis connects the vertices  2b is the length of the conjugate axis, which is perpendicular to the transverse axis  2c is the distance between the foci  The foci lie on the same line as the transverse axis.  (x-h) 2 /a 2 –(y–k) 2 /b 2 =1 or (y–k) 2 /a 2 –(x– h) 2 /b 2 =1  (h, k) is the center of the hyperbola  2a is the length of the transverse axis.  The transverse axis connects the vertices  2b is the length of the conjugate axis, which is perpendicular to the transverse axis  2c is the distance between the foci  The foci lie on the same line as the transverse axis.

How is the hyperbola similar to the ellipse?

How is the hyperbola different than the ellipse?  A hyperbola has two asymptotes  An asymptote is a line the the hyperbola can not cross.  The hyperbola gets infinitely close to the asymptote, but never touches it.  These asymptotes are described by the equations y=k±(b/a)(x–h)  A hyperbola has two asymptotes  An asymptote is a line the the hyperbola can not cross.  The hyperbola gets infinitely close to the asymptote, but never touches it.  These asymptotes are described by the equations y=k±(b/a)(x–h)

Graph x 2 /25–(y–2) 2 /16=1  Graph the asymptotes  Plot the vertices  Use the asymptotes as a guide  How would we graph x 2 /25+(y– 2) 2 /16=1  Graph the asymptotes  Plot the vertices  Use the asymptotes as a guide  How would we graph x 2 /25+(y– 2) 2 /16=1

Homework  Pg 184, #1-11, 21