What is a hyperbola?What is a hyperbola?

Do Now: Define the literary term hyperbole.

Do Now: Define the literary term hyperbole.

What are the conic sections?

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?

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?

What is the equation of a hyperbola?

(x-h)2/a2–(y–k)2/b2=1 or (y–k)2/a2–(x–h)2/b2=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/a2–(y–k)2/b2=1 or (y–k)2/a2–(x–h)2/b2=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 similar to the ellipse?

How is the hyperbola different than 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 x2/25–(y–2)2/16=1Graph x2/25–(y–2)2/16=1

Graph the asymptotes Plot the vertices Use the asymptotes as a guide How would we graph x2/25+(y–

2)2/16=1

Graph the asymptotes Plot the vertices Use the asymptotes as a guide How would we graph x2/25+(y–

2)2/16=1

HomeworkHomework

Pg 184, #1-11, 21 Pg 184, #1-11, 21