Casio fx-CG10 Advanced Operation Manual page 89

Prizm graphing calculator

Hide thumbs Also See for fx-CG10:

Chapter 6: Conic Sections

Investigation 6.2—Long-Distance Radio Navigation (continued)

The general form for a hyperbola, with center at the origin and that opens right and

left is,

represents the slope of the asymptotes. Another value, which is usually

designated as C, represents the distance from the center to a focus. The relationship

among A, B, and C is the Pythagorean relationship, namely, A

Also, 2A represents the constant difference between every point on the hyperbola

and the two foci. To see why, consider the point (A, 0), one of the vertices of the

hyperbola. Its distance from the left focus is A + C and its difference from the right

focus is C – A, therefore the difference is 2A.

Let's suppose two transmitting stations are located 400 miles apart. Based on the

difference in times of the pulses it receives from the two stations, a ship determines

that it is 300 miles closer to Station A than to Station B.

a. How would you orient a coordinate plane, which would be useful in finding

the equation of a hyperbola, on which the ship must be located?

b. Write the equation of the hyperbola on which the ship is located.

c. Graph the hyperbola. Then, identify and graph the asymptotes of the

hyperbola.

d. Assume A remains at (150, 0); explore what happens to the hyperbola as the

value for B changes from 20 to 200 in increments of 20.

, where A represents the distance from the center to a vertex and

+ B

= C