Casio fx-CG10 Advanced Operation Manual page 97

Chapter 6: Conic Sections
Sample Solution—Extracorporeal Shockwave Lithotripsy (continued)
a. Suppose the half ellipse is 106 units long with a height of 28 units. Orient this
ellipse with the center about the origin and determine its equation.
One standard form for the equation of an ellipse is:
where (H,K) is the center, A is the distance from the center to the vertices
along the major axis, and B is the distance from the center to the ends of the
minor axis. In this case, (H, K) is (0, 0).
The major axis is 106 units long, so A = 53 and B is 28. Therefore, the equation
2
x y
is:
532 282
b. Determine where the stone would be and where the source of the
shockwaves should be placed.
From Conic Graphs:
Scroll down until the form of the ellipse you want is displayed.
Input
both H and K.
Press
likely want to adjust the viewing window.
Press
X X min: 60, X X max: 60, Y Y min: 30, and Y Y max: 30, with s s cales of 10 on
both axes. Press
window.
2
1 .
for A,
(DRAW) to view the graph; after viewing the graph, you will
(V-Window)
(DRAW) to view the graph in the defined viewing
for B, and, if necessary,
. and make the following changes:
2 2
x ( H ) y ( K )
2 2
A B
1 ,
for