1. Draw a circle on your piece of patty paper. Mark its center. 2. Mark a point outside the circle. 3. Fold your paper so that the point outside the circle lies on your circle. Crease your paper. 4. Repeat several times (at least 10!) until you see a shape appear.
What does a sonic boom have to do with hyperbolas?
In 1953, a pilot flew over an Air Force Base flying faster than the speed of sound. He damaged every building on the base. As the plane moves faster than the speed of sound, you get a cone-like wave. Where the cone intersects the ground, it is an hyperbola. The sonic boom hits every point on that curve at the same time. No sound is heard outside the curve. The hyperbola is known as the "Sonic Boom Curve." In the picture before, the sonic boom is "visible" due to the humidity .
A hyperbola is. . . hyperbola by rockwellcharland http://en.wikipedia.org/wiki/Hyperbola
Anatomy of a hyperbola The center of a hyperbola is located at ____________. The vertices are located _________ units from the center (unlike an ellipse, a is now always __________________!!)
The segment from vertex to vertex is called the __________________________. It is _______________ units long. The curves (or branches) of the hyperbola are guided by __________________. Their slopes are m =
The foci of the hyperbola are located ____________ units from the center. To find c, use the equation :
Example 1 . Graph the hyperbola. Find the center, vertices, and foci.
Example 2 . Write the equation of the hyperbola with the given values. <ul><li>Vertices: (0, 1) and (6, 1) </li></ul><ul><li>Foci: (-1, 1) and (7, 1) </li></ul>
Example 3. Find the center, vertices, and foci. <ul><li>a. y 2 – x 2 + 6x – 4y = 6 </li></ul>